Abstract
O(logn) rounds has been a well known upper bound for rumor spreading using push&pull in the random phone call model (i.e., uniform gossip in the complete graph). A matching lower bound of Ω(logn) is also known for this special case. Under the assumptions of this model and with a natural addition that nodes can call a partner once they learn its address (e.g., its IP address) we present a new distributed, address-oblivious and robust algorithm that uses push&pull with pointer jumping to spread a rumor to all nodes in only \(O(\sqrt{\log n})\) rounds, w.h.p. This algorithm can also cope with \(F= o(n/2^{\sqrt{\log n}})\) node failures, in which case all but O(F) nodes become informed within \(O(\sqrt{\log n})\) rounds, w.h.p.
This work was partially supported by the Austrian Science Fund (FWF) under contract P25214-N23 “Analysis of Epidemic Processes and Algorithms in Large Networks”.
The main result of this paper emerged from an open problem presented at Dagstuhl Seminar 13042 “Epidemic Algorithms and Processes: From Theory to Applications”.
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References
Avin, C., Lotker, Z., Pignolet, Y.-A., Turkel, I.: From caesar to twitter: Structural properties of elites and rich-clubs. CoRR abs/1111.3374 (2012)
Censor-Hillel, K., Haeupler, B., Kelner, J., Maymounkov, P.: Global computation in a poorly connected world: Fast rumor spreading with no dependence on conductance. In: Proc. 44th ACM Symposium on Theory of Computing, pp. 961–970 (2012)
Chaintreau, A., Fraigniaud, P., Lebhar, E.: Opportunistic spatial gossip over mobile social networks. In: Proc. 1st Workshop on Online Social Networks, pp. 73–78 (2008)
Chung, F., Lu, L.: Connected components in random graphs with a given degree expected sequence. Annals of Combinatorics 6, 125–145 (2002)
Deb, S., Médard, M., Choute, C.: Algebraic gossip: a network coding approach to optimal multiple rumor mongering. IEEE Transactions on Information Theory 52(6), 2486–2507 (2006)
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: Proc. 6th Annual ACM Symposium on Principles of Distributed Computing, pp. 1–12 (1987)
Doerr, B., Fouz, M., Friedrich, T.: Social networks spread rumors in sublogarithmic time. In: Proc. 43rd Annual ACM Symposium on Theory of Computing, pp. 21–30 (2011)
Doerr, B., Friedrich, T., Sauerwald, T.: Quasirandom rumor spreading. In: Proc. 19th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 773–781 (2008)
Feige, U., Peleg, D., Raghavan, P., Upfal, E.: Randomized broadcast in networks. Random Struct. Algorithms 1(4), 447–460 (1990)
Fountoulakis, N., Panagiotou, K., Sauerwald, T.: Ultra-fast rumor spreading in social networks. In: Proc. 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1642–1660 (2012)
Frieze, A.M., Grimmett, G.R.: The shortest-path problem for graphs with random arc-lengths. Discrete Applied Mathematics 10(1), 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, pp. 57–68 (2011)
Gurevich, M., Keidar, I.: Correctness of gossip-based membership under message loss. SIAM Journal on Computing 39(8), 3830–3859 (2010)
Haeupler, B.: Simple, fast and deterministic gossip and rumor spreading. In: Proc. 24th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 705–716 (2013)
Harchol-Balter, M., Leighton, T., Lewin, D.: Resource discovery in distributed networks. In: Proc. 18th Annual ACM symposium on Principles of Distributed Computing, pp. 229–237 (1999)
Karp, R., Schindelhauer, C., Shenker, S., Vöcking, B.: Randomized rumor spreading. In: Proc. 41st Annual Symposium on Foundations of Computer Science, pp. 565–574 (2000)
Kempe, D., Dobra, A., Gehrke, J.: Gossip-based computation of aggregate information. In: Proc. of the 44th Annual IEEE Symposium on Foundations of Computer Science, pp. 482–491 (2003)
Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: Proc. 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 137–146 (2003)
Leighton, F.T.: Introduction to parallel algorithms and architectures. Morgan Kaufmann, San Francisco (1992)
Mahlmann, P., Schindelhauer, C.: Distributed random digraph transformations for peer-to-peer networks. In: Proc. 18th Annual ACM Symposium on Parallelism in Algorithms and Architectures, pp. 308–317 (2006)
Mitzenmacher, M., Upfal, E.: Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press, New York (2005)
Pittel, B.: On spreading a rumor. SIAM Journal on Applied Mathematics 47(1), 213–223 (1987)
Raab, M., Steger, A.: “Balls into bins” - A simple and tight analysis. In: Rolim, J.D.P., Serna, M., Luby, M. (eds.) RANDOM 1998. LNCS, vol. 1518, pp. 159–170. Springer, Heidelberg (1998)
Sauerwald, T.: On mixing and edge expansion properties in randomized broadcasting. Algorithmica 56(1), 51–88 (2010)
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Avin, C., Elsässer, R. (2013). Faster Rumor Spreading: Breaking the logn Barrier. In: Afek, Y. (eds) Distributed Computing. DISC 2013. Lecture Notes in Computer Science, vol 8205. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41527-2_15
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DOI: https://doi.org/10.1007/978-3-642-41527-2_15
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