Ultra-Fast Rumor Spreading in Social Networks [chapter]

Nikolaos Fountoulakis, Konstantinos Panagiotou, Thomas Sauerwald
2012 Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms  
We analyze the popular push-pull protocol for spreading a rumor in networks. Initially, a single node knows of a rumor. In each succeeding round, every node chooses a random neighbor, and the two nodes share the rumor if one of them is already aware of it. We present the first theoretical analysis of this protocol on random graphs that have a power law degree distribution with an arbitrary exponent β > 2. Our main findings reveal a striking dichotomy in the performance of the protocol that
more » ... ds on the exponent of the power law. More specifically, we show that if 2 < β < 3, then the rumor spreads to almost all nodes in Θ(log log n) rounds with high probability. On the other hand, if β > 3, then Ω(log n) rounds are necessary. We also investigate the asynchronous version of the push-pull protocol, where the nodes do not operate in rounds, but exchange information according to a Poisson process with rate 1. Surprisingly, we are able to show that, if 2 < β < 3, the rumor spreads even in constant time, which is much smaller than the typical distance of two nodes. To the best of our knowledge, this is the first result that establishes a gap between the synchronous and the asynchronous protocol. This model was considered by Chung et al., who studied in a series of papers [10] [11] [12] , for fairly general choices of w, several properties of the resulting graphs,
doi:10.1137/1.9781611973099.130 dblp:conf/soda/FountoulakisPS12 fatcat:ais6cbiczrhddm43aovo2jvoji