Asymptotically Optimal Randomized Rumor Spreading

  • Benjamin Doerr
  • Mahmoud Fouz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6756)


We propose a new protocol for the fundamental problem of disseminating a piece of information to all members of a group of n players. It builds upon the classical randomized rumor spreading protocol and several extensions. The main achievements are the following:

Our protocol spreads a rumor from one node to all other nodes in the asymptotically optimal time of (1 + o(1)) log2 n. The whole process can be implemented in a way such that only O(n f(n)) calls are made, where f(n) = ω(1) can be arbitrary.

In spite of these quantities being close to the theoretical optima, the protocol remains relatively robust against failures; for random node failures, our algorithm again comes arbitrarily close to the theoretical optima.

The protocol can be extended to also deal with adversarial node failures. The price for that is only a constant factor increase in the run-time, where the constant factor depends on the fraction of failing nodes the protocol is supposed to cope with. It can easily be implemented such that only O(n) calls to properly working nodes are made.

In contrast to the push-pull protocol by Karp et al. [FOCS 2000], our algorithm only uses push operations, i.e., only informed nodes take active actions in the network. On the other hand, we discard address-obliviousness. To the best of our knowledge, this is the first randomized push algorithm that achieves an asymptotically optimal running time.


Cayley Graph Failed Node Basic Protocol Broadcast Tree Random Geometric Graph 
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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  1. 1.
    Berenbrink, P., Elsässer, R., Friedetzky, T.: Efficient randomized broadcasting in random regular networks with applications in peer-to-peer systems. In: Proc. of 27th ACM Symposium on Principles of Distributed Computation (PODC), pp. 155–164 (2008)Google Scholar
  2. 2.
    Bradonjic, M., Elsässer, R., Friedrich, T., Sauerwald, T., Stauffer, A.: Efficient broadcast on random geometric graphs. In: Proc. of the 21st Annual ACM-SIAM Symp. on Discrete Algorithms (SODA), pp. 1412–1421 (2010)Google Scholar
  3. 3.
    Chierichetti, F., Lattanzi, S., Panconesi, A.: Almost tight bounds for rumour spreading with conductance. In: Proceedings of the 42th ACM Symposium on Theory of Computing (STOC), pp. 399–408 (2010)Google Scholar
  4. 4.
    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: Proceedings of the 6th ACM Symposium on Principles of Distributed Computing (PODC), pp. 1–12 (1987)Google Scholar
  5. 5.
    Doerr, B., Friedrich, T., Sauerwald, T.: Quasirandom rumor spreading. In: Proc. of the 19th ACM-SIAM Symp. on Disc. Alg. (SODA), pp. 773–781 (2008)Google Scholar
  6. 6.
    Doerr, B., Friedrich, T., Sauerwald, T.: Quasirandom rumor spreading: Expanders, push vs. Pull, and robustness. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5555, pp. 366–377. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  7. 7.
    Doerr, B., Fouz, M., Friedrich, T.: Social networks spread rumors in sublogarithmic time. In: To appear in the Proceedings of the 43th ACM Symposium on Theory of Computing, STOC (2011)Google Scholar
  8. 8.
    Elsässer, R.: On the Communication Complexity of Randomized Broadcasting in Random-like Graphs. In: Proceedings of the 18th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 148–157 (2006)Google Scholar
  9. 9.
    Elsässer, R., Sauerwald, T.: Broadcasting vs. Mixing and information dissemination on cayley graphs. In: Thomas, W., Weil, P. (eds.) STACS 2007. LNCS, vol. 4393, pp. 163–174. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  10. 10.
    Elsässer, R., Sauerwald, T.: On the Power of Memory in Randomized Broadcasting. In: Proceedings of the 19th ACM-SIAM Symp. on Disc. Alg. (SODA), pp. 218–227 (2008)Google Scholar
  11. 11.
    Feige, U., Peleg, D., Raghavan, P., Upfal, E.: Randomized broadcast in networks. Random Structures and Algorithms 1, 447–460 (1990)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Fountoulakis, N., Huber, A.: Quasirandom rumor spreading on the complete graph is as fast as randomized rumor spreading. SIAM Journal on Discrete Mathematics 23, 1964–1991 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Frieze, A., Grimmett, G.: The shortest-path problem for graphs with random arc-lengths. Discrete Applied Mathematics 10, 57–77 (1985)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Karp, R., Schindelhauer, C., Shenker, S., Vöcking, B.: Randomized Rumor Spreading. In: Proceedings of the 41st IEEE Symposium on Foundations of Computer Science (FOCS), pp. 565–574 (2000)Google Scholar
  15. 15.
    Kempe, D., Dobra, A., Gehrke, J.: Gossip-based computation of aggregate information. In: Proceedings of the 44th Symposium on Foundations of Computer Science (FOCS), pp. 482–491 (2003)Google Scholar
  16. 16.
    Sauerwald, T.: On mixing and edge expansion properties in randomized broadcasting. In: Tokuyama, T. (ed.) ISAAC 2007. LNCS, vol. 4835, pp. 196–207. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Benjamin Doerr
    • 1
  • Mahmoud Fouz
    • 2
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany
  2. 2.Faculty of Computer ScienceUniversität des SaarlandesSaarbrückenGermany

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