Flavio Chierichetti
ABSTRACT
We show that if a connected graph with $n$ nodes has conductance φ then rumour spreading, also known as randomized broadcast, successfully broadcasts a message within ~O(φ-1 • log n), many rounds with high probability, regardless of the source, by using the PUSH-PULL strategy. The ~O(••) notation hides a polylog φ-1 factor. This result is almost tight since there exists graph of n nodes, and conductance φ, with diameter Ω(φ-1 • log n). If, in addition, the network satisfies some kind of uniformity condition on the degrees, our analysis implies that both both PUSH and PULL, by themselves, successfully broadcast the message to every node in the same number of rounds.
- P. Berenbrink, R. Elsasser and T. Friedetzky. Efficient randomized broadcasting in random regular networks with applications in peer-to-peer systems. Proceedings of PODC, 2006. Google Scholar
Digital Library
- S. P. Boyd, A. Ghosh, B. Prabhakar and D. Shah. Gossip algorithms: design, analysis and applications. IEEE Transactions on Information Theory, 2005.Google Scholar
- F. Chierichetti, S. Lattanzi and A. Panconesi. Rumor Spreading in Social Networks. Proceedings of ICALP, 2009. Google ScholarDigital Library
- F. Chierichetti, S. Lattanzi and A. Panconesi. Rumour Spreading and Graph Conductance. Proceedings of SODA, 2010. Google ScholarDigital Library
- A. J. Demers, D. H. Greene, C. Hauser, W. Irish, J. Larson, S. Shenker, H. E. Sturgis, D. C. Swinehart and D. B. Terry. Epidemic Algorithms for Replicated Database Maintenance. Proceedings of PODC, 1987. Google ScholarDigital Library
- B. Doerr, T. Friedrich and T. Sauerwald. Quasirandom Rumor Spreading. Proceedings of SODA, 2008. Google ScholarDigital Library
- B. Doerr, T. Friedrich and T. Sauerwald. Quasirandom Rumor Spreading: Expanders, Push vs. Pull, and Robustness. Proceedings of ICALP, 2009. Google ScholarDigital Library
- R. Elsasser. On the Communication Complexity of Randomized Broadcasting in Random-like Graphs. Proceedings of SPAA, 2006. Google ScholarDigital Library
- U. Feige, D. Peleg, P. Raghavan and E. Upfal. Randomized Broadcast in Networks. Algorithms, 1990. Google ScholarDigital Library
- T. Friedrich and T. Sauerwald. Near-perfect load balancing by randomized rounding. Proceedings of STOC, 2009. Google ScholarDigital Library
- A. Frieze and G. Grimmett. The shortest-path problem for graphs with random arc-lengths. Algorithms, 1985.Google Scholar
- R. Karp, C. Schindelhauer, S. Shenker and B. Vocking. Randomized Rumor Spreading. Proceedings of FOCS, 2000. Google ScholarDigital Library
- D. Kempe, A. Dobra and J. Gehrke. Gossip-based computation of aggregate information. Proceedings of FOCS, 2003. Google ScholarDigital Library
- J. Leskovec, K. J. Lang, A. Dasgupta and M. W. Mahoney. Statistical properties of community structure in large social and information networks. Proceedings of WWW, 2008. Google ScholarDigital Library
- M. Mihail, C. H. Papadimitriou and A. Saberi. On certain connectivity properties of the Internet topology. J. Comput. Syst. Sci., 2006. Google ScholarDigital Library
- D. Mosk-Aoyama and D. Shah. Fast Distributed Algorithms for Computing Separable Functions. Transactions on Information Theory, 2008. Google ScholarDigital Library
- B. Pittel. On Spreading a Rumor. SIAM Journal on Applied Mathematics, 1987. Google ScholarDigital Library
- T. Sauerwald. On Mixing and Edge Expansion Properties in Randomized Broadcasting. Proceedings of ISAAC, 2007. Google ScholarDigital Library
- D. A. Spielman and S.-H. Teng. Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems. Proceedings of STOC, 2004. Google ScholarDigital Library
Index Terms
- Almost tight bounds for rumour spreading with conductance
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