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Asynchronous Rumor Spreading in Preferential Attachment Graphs

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Algorithm Theory – SWAT 2012 (SWAT 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7357))

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Abstract

We show that the asynchronous push-pull protocol spreads rumors in preferential attachment graphs (as defined by Barabási and Albert) in time \(O(\sqrt{\log n})\) to all but a lower order fraction of the nodes with high probability. This is significantly faster than what synchronized protocols can achieve; an obvious lower bound for these is the average distance, which is known to be Θ(logn/loglogn).

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References

  1. Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)

    Article  MathSciNet  Google Scholar 

  2. Bollobás, B., Riordan, O.: The diameter of a scale-free random graph. Combinatorica 24, 5–34 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bollobás, B., Thomason, A.: On Richardson’s Model on the Hypercube. Cambridge University Press (1997)

    Google Scholar 

  4. 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)

    Article  MathSciNet  MATH  Google Scholar 

  5. Boyd, S., Ghosh, A., Prabhakar, B., Shah, D.: Randomized gossip algorithms. IEEE Transactions on Information Theory 52, 2508–2530 (2006)

    Article  MathSciNet  Google Scholar 

  6. 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 

  7. Chierichetti, F., Lattanzi, S., Panconesi, A.: Rumor spreading in social networks. Theoretical Computer Science 412, 2602–2610 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Chung, F.R.K., Lu, L.: The average distance in a random graph with given expected degrees. Internet Mathematics 1, 91–113 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. 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)

    Article  Google Scholar 

  10. 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, Part I. LNCS, vol. 5555, pp. 366–377. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  11. 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 

  12. Dommers, S., van der Hofstad, R., Hooghiemstray, G.: Diameters in preferential attachment models. Journal of Statistical Physics 139, 72–107 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. 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 

  14. Evans, M., Hastings, N., Peacock, B.: Statistical Distributions, 3rd edn. John Wiley & Sons, Inc. (2000)

    Google Scholar 

  15. Feige, U., Peleg, D., Raghavan, P., Upfal, E.: Randomized broadcast in networks. Random Structures & Algorithms 1, 447–460 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  16. Fill, J.A., Pemantle, R.: Percolation, first-passage percolation, and covering times for Richardson’s model on the n-cube. Annals of Applied Probability 3, 593–629 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  17. Fountoulakis, N., Panagiotou, K.: Rumor Spreading on Random Regular Graphs and Expanders. In: Serna, M., Shaltiel, R., Jansen, K., Rolim, J. (eds.) APPROX and RANDOM 2010, LNCS, vol. 6302, pp. 560–573. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  18. 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 

  19. Frieze, A.M., Grimmett, G.R.: The shortest-path problem for graphs with random arc-lengths. Discrete Applied Mathematics 10, 57–77 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  20. 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 

  21. Janson, S.: One, two and three times logn/n for paths in a complete graph with random weights. Combinatorics, Probability & Computing 8, 347–361 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  22. 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 

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Benjamin Doerr & Tobias Friedrich

  2. Universität des Saarlandes, Saarbrücken, Germany

    Mahmoud Fouz & Tobias Friedrich

Authors
  1. Benjamin Doerr
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  2. Mahmoud Fouz
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  3. Tobias Friedrich
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Editor information

Editors and Affiliations

  1. Institute of Informatics, University of Bergen, Postboks 7800, 5020, Bergen, Norway

    Fedor V. Fomin

  2. Department of Information and Computer Science, Aalto University, PO Box 15400, 00076, Aalto, Finland

    Petteri Kaski

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© 2012 Springer-Verlag Berlin Heidelberg

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Doerr, B., Fouz, M., Friedrich, T. (2012). Asynchronous Rumor Spreading in Preferential Attachment Graphs. In: Fomin, F.V., Kaski, P. (eds) Algorithm Theory – SWAT 2012. SWAT 2012. Lecture Notes in Computer Science, vol 7357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31155-0_27

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  • DOI: https://doi.org/10.1007/978-3-642-31155-0_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31154-3

  • Online ISBN: 978-3-642-31155-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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