Greedy Routing in Tree-Decomposed Graphs

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Greedy Routing in Tree-Decomposed Graphs
Milgram’s experiment (1967) demonstrated that there are short chains of acquaintances between individuals, and that these chains can be discovered in a greedy manner. Kleinberg (2000) gave formal support to this so-called “small world phenomenon” by using meshes augmented with long-range links chosen randomly according to harmonic distributions. In this paper, we propose a new perspective on the small world phenomenon by considering arbitrary graphs augmented according to distributions guided by tree-decompositions of the graphs. We show that, for any n-node graph G of treewidth ≤ k, there exists a tree-decomposition-based distribution D such that greedy routing in the augmented graph (G, D) performs in O(k log2 n) expected number of steps. We argue that augmenting a graph with long-range links chosen according to a tree-decomposition-based distribution is plausible in the context of social networks. However, social networks can have unbounded treewidth. Nevertheless, we note ...
Pierre Fraigniaud
Added 29 Jun 2010
Updated 29 Jun 2010
Type Conference
Year 2005
Where ESA
Authors Pierre Fraigniaud
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