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 ...

• Type: Conference
• Year: 2005
• Where: ESA
• Authors: Pierre Fraigniaud
• Keywords: ESA 2005, Greedy Routing, Small World Phenomenon, Tree-decomposition-based Distribution