Estimating Time Complexity of Rumor Spreading in Ad-Hoc Networks

  • Dariusz R. Kowalski
  • Christopher Thraves Caro
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7960)


Rumor spreading is a fundamental communication process: given a network topology modeled by a graph and a source node with a message, the goal is to disseminate the source message to all network nodes. In this work we give a new graph-based formula that is a relatively tight estimate of the time complexity of rumor spreading in ad-hoc networks by popular Push&Pull protocol. We demonstrate its accuracy by comparing it to previously considered characteristics, such as graph conductance or vertex expansion, which in some cases are even exponentially worse than our new characterization.


Rumor spreading conductance vertex expansion synchronous model asynchronous model Push&Pull protocol 


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  1. 1.
    Avin, C., Borokhovich, M., Censor-Hillel, K., Lotker, Z.: Order optimal information spreading using algebraic gossip. In: Proceedings of PODC 2011, pp. 363–372 (2011)Google Scholar
  2. 2.
    Censor-Hillel, K., Haeupler, B., Kelner, J.A., Maymounkov, P.: Global computation in a poorly connected world: fast rumor spreading with no dependence on conductance. In: Proceedings of STOC 2012, pp. 961–970 (2012)Google Scholar
  3. 3.
    Censor-Hillel, K., Shachnai, H.: Partial information spreading with application to distributed maximum coverage. In: Proceedings of PODC 2010, pp. 161–170 (2010)Google Scholar
  4. 4.
    Censor-Hillel, K., Shachnai, H.: Fast information spreading in graphs with large weak conductance. In: Proceedings of SODA 2011, pp. 440–448 (2011)Google Scholar
  5. 5.
    Chierichetti, F., Lattanzi, S., Panconesi, A.: Almost tight bounds for rumour spreading with conductance. In: Proceedings of STOC 2010, pp. 399–408 (2010)Google Scholar
  6. 6.
    Chierichetti, F., Lattanzi, S., Panconesi, A.: Rumour spreading and graph conductance. In: Proceedings of SODA 2010, pp. 1657–1663 (2010)Google Scholar
  7. 7.
    Chierichetti, F., Lattanzi, S., Panconesi, A.: Rumor spreading in social networks. Theor. Comput. Sci. 412(24), 2602–2610 (2011)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Demers, A., Greene, D., Houser, C., Irish, W., Larson, J., Shenker, S., Sturgis, H., Swinehart, D., Terry, D.: Epidemic algorithms for replicated database maintenance. SIGOPS Oper. Syst. Rev. 22, 8–32 (1988)CrossRefGoogle Scholar
  9. 9.
    Doerr, B., Fouz, M.: Asymptotically optimal randomized rumor spreading. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 502–513. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  10. 10.
    Doerr, B., Fouz, M., Friedrich, T.: Social networks spread rumors in sublogarithmic time. In: Proceedings of STOC 2011, pp. 21–30 (2011)Google Scholar
  11. 11.
    Dolev, S., Schiller, E., Welch, J.L.: Random walk for self-stabilizing group communication in ad hoc networks. IEEE Trans. Mob. Comput. 5(7), 893–905 (2006)CrossRefGoogle Scholar
  12. 12.
    Elsässer, R.: On the communication complexity of randomized broadcasting in random-like graphs. In: Proceedings of SPAA 2006, pp. 148–157 (2006)Google Scholar
  13. 13.
    Fountoulakis, N., Panagiotou, K., Sauerwald, T.: Ultra-fast rumor spreading in social networks. In: Proceedings of SODA 2012, pp. 1642–1660 (2012)Google Scholar
  14. 14.
    Giakkoupis, G.: Tight bounds for rumor spreading in graphs of a given conductance. In: Proceedings of STACS 2011, pp. 57–68 (2011)Google Scholar
  15. 15.
    Giakkoupis, G., Sauerwald, T.: Rumor spreading and vertex expansion. In: Proceedings of SODA 2012, pp. 1623–1641 (2012)Google Scholar
  16. 16.
    Hromkovic, J., Klasing, R., Pelc, A., Ruzicka, P., Unger, W.: Dissemination of Information in Communication Networks: Broadcasting, Gossiping, Leader Election, and Fault-Tolerance. Texts in Theoretical Computer Science. An EATCS Series. Springer (2010)Google Scholar
  17. 17.
    Karp, R.M., Schindelhauer, C., Shenker, S., Vocking, B.: Randomized rumor spreading. In: Proceedings of FOCS 2000, pp. 565–574 (2000)Google Scholar
  18. 18.
    Mosk-Aoyama, D., Shah, D.: Fast distributed algorithms for computing separable functions. IEEE Transactions on Information Theory 54(7), 2997–3007 (2008)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Sauerwald, T.: On mixing and edge expansion properties in randomized broadcasting. Algorithmica 56, 51–88 (2010)MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Sauerwald, T., Stauffer, A.: Rumor spreading and vertex expansion on regular graphs. In: Proceedings of SODA 2011, pp. 462–475 (2011)Google Scholar
  21. 21.
    Sinclair, A.: Algorithms for random generation and counting - a Markov chain approach. Progress in theoretical computer science. Birkhäuser (1993)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Dariusz R. Kowalski
    • 1
  • Christopher Thraves Caro
    • 2
  1. 1.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK
  2. 2.GSyCUniversidad Rey Juan CarlosSpain

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