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Graph Augmentation via Metric Embedding
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BibTeX
@MISC{Lebhar_graphaugmentation,
author = {Emmanuelle Lebhar and Nicolas Schabanel},
title = {Graph Augmentation via Metric Embedding},
year = {}
}
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Abstract
Abstract. Kleinberg [17] proposed in 2000 the first random graph model achieving to reproduce small world navigability, i.e. the ability to greedily discover polylogarithmic routes between any pair of nodes in a graph, with only a partial knowledge of distances. Following this seminal work, a major challenge was to extend this model to larger classes of graphs than regular meshes, introducing the concept of augmented graphs navigability. In this paper, we propose an original method of augmentation, based on metrics embeddings. Precisely, we prove that, for any ε>0, any graph G such that its shortest paths metric admits an embedding of distorsion γ into R d can be augmented by one link per node such that greedy routing computes paths of expected length O ( 1 ε γd log 2+ε n) between any pair of nodes with the only knowledge of G. Ourmethod isolates all the structural constraints in the existence of a good quality embedding and therefore enables to enlarge the characterization of augmentable graphs.
Keyphrases
metric embedding graph augmentation augmented graph navigability seminal work small world navigability polylogarithmic route path metric admits partial knowledge computes path regular mesh good quality structural constraint first random graph model original method augmentable graph metric embeddings major challenge
