NDLI: On the searchability of small-world networks with arbitrary underlying structure

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On the searchability of small-world networks with arbitrary underlying structure

Content Provider	ACM Digital Library
Author	Fraigniaud, Pierre Giakkoupis, George
Abstract	Revisiting the "small-world" experiments of the '60s, Kleinberg observed that individuals are very effective at constructing short chains of acquaintances between any two people, and he proposed a mathematical model of this phenomenon. In this model, individuals are the nodes of a base graph, the square grid, capturing the underlying structure of the social network; and this base graph is augmented with additional edges from each node to a few long-range contacts of this node, chosen according to some natural distance-based distribution. In this augmented graph, a greedy search algorithm takes only a polylogarithmic number of steps in the graph size. Following this work, several papers investigated the correlations between underlying structure and long-range connections that yield efficient decentralized search, generalizing Kleinberg's results to broad classes of underlying structures, such as metrics of bounded doubling dimension, and minor-excluding graphs. We focus on the case of arbitrary base graphs. We show that for a simple long-range contact distribution consistent with empirical observations on social networks, a slight variation of greedy search, where the next hop is to a distant node only if it yields sufficient progress towards the target, requires $n^{o(1)}$ steps, where \$n\$ is the number of nodes. Precisely, the expected number of steps for any source-target pair is at most 2(log $n)^{1/2+o(1)}}.$ This bound almost matches the best known lower bound of Ω(2√log n) steps, which applies to a general class of search algorithms. In the context of social networks, our result could be interpreted as: individuals may well be able to construct short chains between people regardless of the underlying structure of the social network.
Starting Page	389
Ending Page	398
Page Count	10
File Format	PDF
ISBN	9781450300506
DOI	10.1145/1806689.1806744
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2010-06-05
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Decentralized search Social networks Small worlds
Content Type	Text
Resource Type	Article

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