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Isoperimetric Inequalities for Cartesian Products of Graphs
Combinatorics, Probability and Computing
On the spread of viruses on the internet
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On certain connectivity properties of the internet topology
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Rumor Spreading in Social Networks
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
A gossip-style failure detection service
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Almost tight bounds for rumour spreading with conductance
Proceedings of the forty-second ACM symposium on Theory of computing
Reliable broadcasting in random networks and the effect of density
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Rumour spreading and graph conductance
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Rumor spreading on random regular graphs and expanders
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Social networks spread rumors in sublogarithmic time
Proceedings of the forty-third annual ACM symposium on Theory of computing
Fast information spreading in graphs with large weak conductance
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Rumor spreading and vertex expansion on regular graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Fast Distributed Algorithms for Computing Separable Functions
IEEE Transactions on Information Theory
The power of local information in social networks
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Strong robustness of randomized rumor spreading protocols
Discrete Applied Mathematics
Coalescing-branching random walks on graphs
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
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We study the relation between the rate at which rumors spread throughout a graph and the vertex expansion of the graph. We consider the standard rumor spreading protocol where every node chooses a random neighbor in each round and the two nodes exchange the rumors they know. For any n-node graph with vertex expansion α, we show that this protocol spreads a rumor from a single node to all other nodes in [EQUATION] rounds with high probability. Further, we construct graphs for which Ω(α−1 log2 n) rounds are needed. Our results complement a long series of works that relate rumor spreading to edge-based notions of expansion, resolving one of the most natural questions on the connection between rumor spreading and expansion.