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Rumor spreading and vertex expansion (2012)
| Venue: | In SODA |
| Citations: | 15 - 2 self |
BibTeX
@INPROCEEDINGS{Giakkoupis12rumorspreading,
author = {George Giakkoupis and Thomas Sauerwald},
title = {Rumor spreading and vertex expansion},
booktitle = {In SODA},
year = {2012},
pages = {1623--1641}
}
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Abstract
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 2 n √ log n) rounds with high probability. Further, we construct graphs for which Ω(α −1 log 2 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. 1
