Quasirandom Rumor Spreading: Expanders, Push vs. Pull, and Robustness

Randomized rumor spreading is an efficient protocol to distribute information in networks. Recently, a quasirandom version has been proposed and proven to work equally well on many graphs and better for sparse random graphs. In this work we show three main results for the quasirandom rumor spreading model. We exhibit a natural expansion property for networks which suffices to make quasirandom rumor spreading inform all nodes of the network in logarithmic time with high probability. This expansion property is satisfied, among others, by many expander graphs, random regular graphs, and Erdős-Renyi random graphs. For all network topologies, we show that if one of the push or pull model works well, so does the other. We also show that quasirandom rumor spreading is robust against transmission failures. If each message sent out gets lost with probability f , then the runtime increases only by a factor of $\O(1/(1-f))$.

[1]  Thomas Sauerwald,et al.  On Mixing and Edge Expansion Properties in Randomized Broadcasting , 2007, Algorithmica.

[2]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[3]  Arthur L. Liestman,et al.  A survey of gossiping and broadcasting in communication networks , 1988, Networks.

[4]  Alan M. Frieze,et al.  The shortest-path problem for graphs with random arc-lengths , 1985, Discret. Appl. Math..

[5]  Andrzej Pelc,et al.  Dissemination of Information in Communication Networks - Broadcasting, Gossiping, Leader Election, and Fault-Tolerance , 2005, Texts in Theoretical Computer Science. An EATCS Series.

[6]  Joel Friedman,et al.  On the second eigenvalue and random walks in randomd-regular graphs , 1991, Comb..

[7]  Johannes Gehrke,et al.  Gossip-based computation of aggregate information , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[8]  Richard M. Karp,et al.  Randomized rumor spreading , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[9]  Thomas Sauerwald,et al.  On the runtime and robustness of randomized broadcasting , 2006, Theor. Comput. Sci..

[10]  Scott Shenker,et al.  Epidemic algorithms for replicated database maintenance , 1988, OPSR.

[11]  N. Linial,et al.  Expander Graphs and their Applications , 2006 .

[12]  Thomas Sauerwald,et al.  Quasirandom rumor spreading , 2008, SODA '08.

[13]  Alan M. Frieze,et al.  The cover time of sparse random graphs. , 2003, SODA '03.

[14]  Thomas Sauerwald,et al.  Quasirandom rumor spreading: An experimental analysis , 2008, JEAL.

[15]  Eli Upfal,et al.  Randomized Broadcast in Networks , 1990, Random Struct. Algorithms.

[16]  B. Pittel.  On spreading a rumor , 1987 .