Searching for Nodes in Random Graphs

Details Searching for Nodes in Random Graphs Searching for Nodes in Random Graphs

2011-08-24

arxiv.org/abs/1108.4785v1

Physics

Condensed Matter

Statistical Mechanics

13 pages, 12 figures

Scientific paper

We consider the problem of searching for a node on a labelled random graph according to a greedy algorithm that selects a route to the desired node using metric information on the graph. Motivated by peer-to-peer networks two types of random graph are proposed with properties particularly amenable to this kind of algorithm. We derive equations for the probability that the search is successful and also study the number of hops required, finding both numerical and analytic evidence of a transition as the number of links is varied.

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