Local Update Algorithms for Random Graphs

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


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.


random graphs dynamic graphs logical network maintenance randomness preservation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Frankel, J., Pepper, T.: The gnutella project,
  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

Personalised recommendations