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).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)
Bollobás, B., Riordan, O.: The diameter of a scale-free random graph. Combinatorica 24, 5–34 (2004)
Bollobás, B., Thomason, A.: On Richardson’s Model on the Hypercube. Cambridge University Press (1997)
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)
Boyd, S., Ghosh, A., Prabhakar, B., Shah, D.: Randomized gossip algorithms. IEEE Transactions on Information Theory 52, 2508–2530 (2006)
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)
Chierichetti, F., Lattanzi, S., Panconesi, A.: Rumor spreading in social networks. Theoretical Computer Science 412, 2602–2610 (2011)
Chung, F.R.K., Lu, L.: The average distance in a random graph with given expected degrees. Internet Mathematics 1, 91–113 (2003)
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)
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)
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)
Dommers, S., van der Hofstad, R., Hooghiemstray, G.: Diameters in preferential attachment models. Journal of Statistical Physics 139, 72–107 (2010)
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)
Evans, M., Hastings, N., Peacock, B.: Statistical Distributions, 3rd edn. John Wiley & Sons, Inc. (2000)
Feige, U., Peleg, D., Raghavan, P., Upfal, E.: Randomized broadcast in networks. Random Structures & Algorithms 1, 447–460 (1990)
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)
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)
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)
Frieze, A.M., Grimmett, G.R.: The shortest-path problem for graphs with random arc-lengths. Discrete Applied Mathematics 10, 57–77 (1985)
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)
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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)