Rumor spreading and vertex expansion
نویسندگان
چکیده
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 O(α−1 log n √ logn) rounds with high probability. Further, we construct graphs for which Ω(α−1 log n) rounds are needed. Our results complement a long series of works that relate rumor spreading to edgebased notions of expansion, resolving one of the most natural questions on the connection between rumor spreading and expansion.
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