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Global Computation in a Poorly Connected World: Fast Rumor Spreading with No Dependence on Conductance (2012)
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BibTeX
@MISC{Censor-hillel12globalcomputation,
author = {Keren Censor-hillel and Bernhard Haeupler and Jonathan A. Kelner and Petar Maymounkov},
title = {Global Computation in a Poorly Connected World: Fast Rumor Spreading with No Dependence on Conductance },
year = {2012}
}
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Abstract
In this paper, we study the question of how efficiently a collection of interconnected nodes can perform a global computation in the GOSSIP model of communication. In this model, nodes do not know the global topology of the network, and they may only initiate contact with a single neighbor in each round. This model contrasts with the much less restrictive LOCAL model, where a node may simultaneously communicate with all of its neighbors in a single round. A basic question in this setting is how many rounds of communication are required for the information dissemination problem, in which each node has some piece of information and is required to collect all others. In the LOCAL model, this is quite simple: each node broadcasts all of its information in each round, and the number of rounds required will be equal to the diameter of the underlying communication graph. In the GOSSIP model, each node must independently choose a single neighbor to contact, and the lack of global information makes it difficult to make any sort of principled choice. As such, researchers have focused on the uniform gossip algorithm, in which each node independently selects a neighbor uniformly at random. When the graph is well-connected, this works quite well. In a string of beautiful papers, researchers proved a sequence of successively stronger bounds on the number of rounds required in terms of the conductance φ and graph size n, culminating in a bound of O(φ −1 log n). In this paper, we show that a fairly simple modification of the protocol gives an algorithm that solves the information dissemination problem in at most O(D + polylog(n)) rounds in a network of diameter D, with no dependence on the conductance. This is
Keyphrases
global computation fast rumor gossip model information dissemination problem single neighbor basic question global information restrictive local model principled choice simple modification single round beautiful paper many round global topology local model interconnected node underlying communication graph uniform gossip algorithm graph size
