Experimental Analysis of Rumor Spreading in Social Networks

  • Benjamin Doerr
  • Mahmoud Fouz
  • Tobias Friedrich
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7659)

Abstract

Randomized rumor spreading was recently shown to be a very efficient mechanism to spread information in preferential attachment networks. Most interesting from the algorithm design point of view was the observation that the asymptotic run-time drops when memory is used to avoid re-contacting neighbors within a small number of rounds.

In this experimental investigation, we confirm that a small amount of memory indeed reduces the run-time of the protocol even for small network sizes. We observe that one memory cell per node suffices to reduce the run-time significantly; more memory helps comparably little. Aside from extremely sparse graphs, preferential attachment graphs perform faster than all other graph classes examined. This holds independent of the amount of memory, but preferential attachment graphs benefit the most from the use of memory. We also analyze the influence of the network density and the size of the memory. For the asynchronous version of the rumor spreading protocol, we observe that the theoretically predicted asymptotic advantage of preferential attachment graphs is smaller than expected. There are other topologies which benefit even more from asynchrony.

We complement our findings on artificial network models by the corresponding experiments on crawls of popular online social networks, where again we observe extremely rapid information dissemination and a sizable benefit from using memory and asynchrony.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Baumann, H., Fraigniaud, P., Harutyunyan, H.A., de Verclos, R.: The Worst Case Behavior of Randomized Gossip. In: Agrawal, M., Cooper, S.B., Li, A. (eds.) TAMC 2012. LNCS, vol. 7287, pp. 330–345. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  3. 3.
    Berger, N., Borgs, C., Chayes, J.T., Saberi, A.: On the spread of viruses on the Internet. In: 16th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 301–310 (2005)Google Scholar
  4. 4.
    Bhattacharjee, B., Druschel, P., Gummadi, K., et al.: Online social networks research at the Max Planck Institute for Software Systems, http://socialnetworks.mpi-sws.org
  5. 5.
    Bohman, T., Frieze, A.M.: Hamilton cycles in 3-out. Random Structures & Algorithms 35, 393–417 (2009)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Bollobás, B., Riordan, O.: Robustness and vulnerability of scale-free random graphs. Internet Mathematics 1, 1–35 (2003)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Bollobás, B., Riordan, O.: Coupling scale-free and classical random graphs. Internet Mathematics 1, 215–225 (2003b)CrossRefGoogle Scholar
  8. 8.
    Bollobás, B., Riordan, O.: The diameter of a scale-free random graph. Combinatorica 24, 5–34 (2004)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Bollobás, B., Riordan, O., Spencer, J., Tusnády, G.: The degree sequence of a scale-free random graph process. Random Structures & Algorithms 18, 279–290 (2001)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Boyd, S., Ghosh, A., Prabhakar, B., Shah, D.: Randomized gossip algorithms. IEEE Transactions on Information Theory 52, 2508–2530 (2006)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Censor-Hillel, K., Shachnai, H.: Fast information spreading in graphs with large weak conductance. In: 22nd ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 440–448 (2011)Google Scholar
  12. 12.
    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: 44th ACM Symposium on Theory of Computing (STOC), pp. 961–970 (2012)Google Scholar
  13. 13.
    Cha, M., Haddadi, H., Benevenuto, F., Gummadi, P.K.: Measuring user influence in Twitter: The million follower fallacy. In: 4th International AAAI Conference on Weblogs and Social Media, ICWSM (2010)Google Scholar
  14. 14.
    Chierichetti, F., Lattanzi, S., Panconesi, A.: Rumour spreading and graph conductance. In: 21st ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1657–1663 (2010)Google Scholar
  15. 15.
    Chierichetti, F., Lattanzi, S., Panconesi, A.: Almost tight bounds for rumour spreading with conductance. In: 42nd ACM Symposium on Theory of Computing (STOC), pp. 399–408 (2010)Google Scholar
  16. 16.
    Chierichetti, F., Lattanzi, S., Panconesi, A.: Rumor spreading in social networks. Theoretical Computer Science 412, 2602–2610 (2011)MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Chung, F.R.K., Lu, L.: The average distance in a random graph with given expected degrees. Internet Mathematics 1, 91–113 (2003)MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Cooper, C., Frieze, A.M.: The cover time of the preferential attachment graph. Journal of Combinatorial Theory, Series B 97, 269–290 (2007)MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Demers, A.J., Greene, D.H., Hauser, C., Irish, W., Larson, J., Shenker, S., Sturgis, H.E., Swinehart, D.C., Terry, D.B.: Epidemic algorithms for replicated database maintenance. Operating Systems Review 22, 8–32 (1988)CrossRefGoogle Scholar
  20. 20.
    Doerr, B., Friedrich, T., Sauerwald, T.: Quasirandom rumor spreading. In: 19th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 773–781 (2008)Google Scholar
  21. 21.
    Doerr, B., Friedrich, T., Künnemann, M., Sauerwald, T.: Quasirandom rumor spreading: An experimental analysis. In: 10th Workshop on Algorithm Engineering and Experiments (ALENEX), pp. 145–153 (2009)Google Scholar
  22. 22.
    Doerr, B., Fouz, M., Friedrich, T.: Social networks spread rumors in sublogarithmic time. In: 43rd ACM Symposium on Theory of Computing (STOC), pp. 21–30 (2011)Google Scholar
  23. 23.
    Doerr, B., Fouz, M., Friedrich, T.: Asynchronous Rumor Spreading in Preferential Attachment Graphs. In: Fomin, F.V., Kaski, P. (eds.) SWAT 2012. LNCS, vol. 7357, pp. 307–315. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  24. 24.
    Dommers, S., van der Hofstad, R., Hooghiemstray, G.: Diameters in preferential attachment models. J. of Statistical Physics 139, 72–107 (2010)MATHCrossRefGoogle Scholar
  25. 25.
    Elsässer, R.: On the communication complexity of randomized broadcasting in random-like graphs. In: 18th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 148–157 (2006)Google Scholar
  26. 26.
    Elsässer, R., Sauerwald, T.: On the power of memory in randomized broadcasting. In: 19th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 218–227 (2008)Google Scholar
  27. 27.
    Feige, U., Peleg, D., Raghavan, P., Upfal, E.: Randomized broadcast in networks. Rand. Struct. & Algo. 1, 447–460 (1990)MathSciNetMATHCrossRefGoogle Scholar
  28. 28.
    Flaxman, A.D., Frieze, A.M., Vera, J.: Adversarial deletion in a scale-free random graph process. Comb., Probab. & Comput. 16, 261–270 (2007)MathSciNetMATHCrossRefGoogle Scholar
  29. 29.
    Fountoulakis, N., Panagiotou, K., Sauerwald, T.: Ultra-fast rumor spreading in social networks. In: 23rd ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1642–1660 (2012)Google Scholar
  30. 30.
    Frieze, A.M., Grimmett, G.R.: The shortest-path problem for graphs with random arc-lengths. Discrete Applied Mathematics 10, 57–77 (1985)MathSciNetMATHCrossRefGoogle Scholar
  31. 31.
    Giakkoupis, G.: Tight bounds for rumor spreading in graphs of a given conductance. In: 28th International Symposium on Theoretical Aspects of Computer Science (STACS), pp. 57–68 (2011)Google Scholar
  32. 32.
    Karp, R., Schindelhauer, C., Shenker, S., Vöcking, B.: Randomized rumor spreading. In: 41st IEEE Symposium on Foundations of Computer Science (FOCS), pp. 565–574 (2000)Google Scholar
  33. 33.
    Kempe, D., Dobra, A., Gehrke, J.: Gossip-based computation of aggregate information. In: 44th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 482–491 (2003)Google Scholar
  34. 34.
    Kempe, D., Kleinberg, J.M., Demers, A.J.: Spatial gossip and resource location protocols. J. ACM 51(6), 943–967 (2004)MathSciNetMATHCrossRefGoogle Scholar
  35. 35.
    Mislove, A., Marcon, M., Gummadi, K.P., Druschel, P., Bhattacharjee, B.: Measurement and analysis of online social networks. In: 7th ACM SIGCOMM Conference on Internet Measurement (IMC), pp. 29–42 (2007)Google Scholar
  36. 36.
    Pittel, B.: On spreading a rumor. SIAM Journal on Applied Mathematics 47, 213–223 (1987)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Benjamin Doerr
    • 1
  • Mahmoud Fouz
    • 2
  • Tobias Friedrich
    • 3
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany
  2. 2.Rocket InternetDubaiU.A.E.
  3. 3.Friedrich-Schiller-Universität JenaGermany

Personalised recommendations