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Asynchronous Rumor Spreading on Random Graphs

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Abstract

We perform a thorough study of various characteristics of the asynchronous push–pull protocol for spreading a rumor on Erdős–Rényi random graphs \(G_{n,p}\), for any \(p>c\ln (n)/n\) with \(c>1\). In particular, we provide a simple strategy for analyzing the asynchronous push–pull protocol on arbitrary graph topologies and apply this strategy to \(G_{n,p}\). We prove tight bounds of logarithmic order for the total time that is needed until the information has spread to all nodes. Surprisingly, the time required by the asynchronous push–pull protocol is asymptotically almost unaffected by the average degree of the graph. Similarly tight bounds for Erdős–Rényi random graphs have previously only been obtained for the synchronous push protocol, where it has been observed that the total running time increases significantly for sparse random graphs. Finally, we quantify the robustness of the protocol with respect to transmission and node failures. Our analysis suggests that the asynchronous protocols are particularly robust with respect to these failures compared to their synchronous counterparts.

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Notes

  1. This observation was also made in [25].

References

  1. Acan, H., Collevecchio, A., Mehrabian, A., Wormald, N.: On the push and pull protocol for rumour spreading. arXiv:1411.0948

  2. Aigner, M., Ziegler, G.: Proofs from the Book. Springer, Berlin (2010)

    Book  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  4. Bollobás, B.: Random Graphs, Cambridge Studies in Advanced Mathematics, vol. 73, 2nd edn. Cambridge University Press, Cambridge (2001)

    Book  Google Scholar 

  5. Bollobás, B., Kohayakawa, Y.: On Richardsons Model on the Hypercube. Cambridge University Press, Cambridge (1997)

    MATH  Google Scholar 

  6. Boyd, S., Arpita, G., Balaji, P., Devavrat, S.: Gossip algorithms: Design, analysis and applications. In: Proceedings of the 24th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM’05), pp. 1653–1664. Miami, FL, USA (2005)

  7. Boyd, S., Ghosh, A., Prabhakar, B., Shah, D.: Randomized gossip algorithms. IEEE Trans. Inf. Theory 52, 2508–2530 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Chierichetti, F., Lattanzi, S., Panconesi, A.: Almost tight bounds for rumour spreading with conductance. In: Proceedings of the 42nd ACM Symposium on Theory of Computing (STOC ’10), pp. 399–408. Cambridge, MA, USA (2010)

  9. Chierichetti, F., Lattanzi, S., Panconesi, A.: Rumour spreading and graph conductance. In: Proceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’10), pp. 1657–1663. Austin, TX, USA (2010)

  10. Chung, F., Lu, L.: The average distance in a random graph with given expected degrees. Proc Natl Acad Sci USA 99, 15879–15882 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Cooper, C., Frieze, A.: The cover time of sparse random graphs. Random Struct. Algorithms 30, 1–16 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. 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 Annual ACM Symposium on Principles of Distributed Computing (POCD’87), pp. 1–12. Vancouver, BC, Canada (1987)

  13. Doerr, B., Fouz, M., Friedrich, T.: Social networks spread rumors in sublogarithmic time. Electron Notes Discret. Math. 38, 303–308 (2011)

    Article  MATH  Google Scholar 

  14. Doerr, B., Fouz, M., Friedrich, T.: Asynchronous rumor spreading in preferential attachment graphs. In: Proceedings of the 13th Scandinavian Workshop on Algorithm Theory (SWAT’12), pp. 307–315. Helsinki, Finland (2012)

  15. Feller, W.: An Introduction to Probability Theory and Its Applications, vol. 1. Wiley, New York, NY (1968)

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  17. Fountoulakis, N., Huber, A., Panagiotou, K.: Reliable broadcasting in random networks and the effect of density. In: Proceedings of the 29th Conference on Computer Communications (INFOCOM ’10), pp. 2552–2560. San Diego, CA, USA (2010)

  18. Fountoulakis, N., Panagiotou, K., Sauerwald, T.: Ultra-fast rumor spreading in social networks. In: Proceedings of the 23rd ACM-SIAM Symposium on Discrete Algorithms (SODA ’12), pp. 1642–1660. Kyoto, Japan (2012)

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

    Article  MathSciNet  MATH  Google Scholar 

  20. Giakkoupis, G.: Tight bounds for rumor spreading in graphs of a given conductance. In: Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS’11), pp. 57–68. Dortmund, Germany (2011)

  21. Janson, S.: One, two and three times log n/n for paths in a complete graph with random weights. Comb. Probab. Comput. 8, 347–361 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  22. Jelasity, M., Voulgaris, S., Guerraoui, R., Kermarrec, A.M., van Steen, M.: Gossip-based peer sampling. ACM Trans. Comput. Syst. 25, 8 (2007)

    Article  Google Scholar 

  23. Karp, R., Schindelhauer, C., Shenker, S., Vöcking, B.: Randomized rumor spreading. In: Proceedings of the 41th Annual Symposium on Foundations of Computer Science (FOCS’00), pp. 565–574. Redondo Beach, CA, USA (2000)

  24. Panagiotou, K., Fountoulakis, N.: Rumor spreading on random regular graphs and expanders. Random Struct. Algorithms 43, 201–220 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  25. Panagiotou, K., Pérez-Giménez, X., Sauerwald, T., Sun, H.: Randomized rumour spreading: the effect of the network topology. Comb. Probab. Comput. 24, 457–479 (2015)

    Article  MathSciNet  Google Scholar 

  26. Panagiotou, K., Speidel, L.: Asynchronous rumor spreading on random graphs. In: Proceedings of the 24th International Symposium on Algorithms and Computation (ISAAC’13), pp. 424–434. Hong Kong, China (2013)

  27. Pittel, B.: On spreading a rumor. SIAM J. Appl. Math. 47, 213–223 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  28. van Renesse, R., Minsky, Y., Hayden, M.: A gossip-style failure detection service. In: Proceedings of the IFIP International Conference on Distributed Systems Platforms and Open Distributed Processing (Middleware’98), pp. 55–70. The Lake District, UK (1998)

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Authors and Affiliations

  1. Mathematics Institute, University of Munich, Theresienstr. 39, 80333, Munich, Germany

    K. Panagiotou

  2. Doctoral Training Centre in Systems Biology, University of Oxford, Rex Richards Building, South Parks Road, Oxford, OX1 3QU, UK

    L. Speidel

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  1. K. Panagiotou
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  2. L. Speidel
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Correspondence to L. Speidel.

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An extended abstract of this paper has been published in the proceedings of the 24th International Symposium on Algorithms and Computation (ISAAC ’13).

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Panagiotou, K., Speidel, L. Asynchronous Rumor Spreading on Random Graphs. Algorithmica 78, 968–989 (2017). https://doi.org/10.1007/s00453-016-0188-x

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  • DOI: https://doi.org/10.1007/s00453-016-0188-x

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