# Fast Information Spreading in Graphs with Large Weak Conductance

## Abstract

*information spreading*among $n$ nodes of a network, where each node $v$ has a message $m(v)$ which must be received by all other nodes. The time required for information spreading has been previously upper-bounded with an inverse relationship to the conductance of the underlying communication graph. This implies high running time bounds for graphs with small conductance. The main contribution of this paper is an information spreading algorithm which overcomes communication bottlenecks and thus achieves fast information spreading for a wide class of graphs, despite their small conductance. As a key tool in our study we use the recently defined concept of

*weak conductance*, a generalization of classic graph conductance which measures how well-connected the components of a graph are. Our hybrid algorithm, which alternates between random and deterministic communication phases, exploits the connectivity within components by first applying

*partial information spreading*, in which information is exchanged within well-connected components, and then sending messages across bottlenecks, thus spreading further throughout the network. This yields substantial improvements over the best known running times of algorithms for information spreading on any graph that has large weak conductance, from a polynomial to a polylogarithmic number of rounds.

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#### History

**Submitted**: 23 August 2011

**Accepted**: 17 September 2012

**Published online**: 15 November 2012

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