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Theses

Algorithmes de routage et modèles aléatoires pour les graphes petits mondes

Abstract : The purpose of this thesis is to study the algorithmic aspects of the small world phenomenon in large interaction networks. Experimental observations showed that large interactions networks (e.g. social or computer networks)
share common global properties. One of them is the small world phenomenon which consists in the existence of very short paths between any pair of nodes, that can be discovered using only a partial knowledge of the network. We are interested in this algorithmic characteristic of the small world effect, its application to decentralized routing, and its emergence in real networks.

We propose a new decentralized routing algorithm on the Kleinberg random graph model of small world, which computes paths of length O(log n.(loglog n)^2), asymptotically shorter than those computed by existing algorithms (O((log n)^2)). This algorithm could be used in peer-peer networks. We develop this study by comparing the edge load induced by the various algorithms proposed on this model.

By trying to exhibit the minimal characteristics of a graph required to turn it into a small world by adding random shortcuts, we propose a new small world model which generalizes Kleinberg's one. It consists in adding a distribution of links depending on the ball sizes of the underlying graph metric. Furthermore, this model can be simply extended to produce any degree distribution, including in particular the famous power-law. Finally, we propose the first distributed scheme which turns a network into a small world by adding one link per node; this is a first step towards the understanding of the emergence of the small world phenomenon in real networks.
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https://tel.archives-ouvertes.fr/tel-00011646
Contributor : Emmanuelle Lebhar <>
Submitted on : Sunday, February 19, 2006 - 8:52:44 PM
Last modification on : Wednesday, November 20, 2019 - 3:06:36 AM
Long-term archiving on: : Monday, September 17, 2012 - 12:06:00 PM

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Emmanuelle Lebhar. Algorithmes de routage et modèles aléatoires pour les graphes petits mondes. Réseaux et télécommunications [cs.NI]. Ecole normale supérieure de lyon - ENS LYON, 2005. Français. ⟨tel-00011646⟩

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