Universal augmentation schemes for network navigability: Overcoming the √n-barrier

Pierre Fraigniaud, Cyril Gavoille, Adrian Kosowski, Emmanuelle Lebhar, Zvi Lotker

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    20 Scopus citations

    Abstract

    Augmented graphs were introduced for the purpose of analyzing the "six degrees of separation between individuals" observed experimentally by the sociologist Standley Milgram in the 60's. Formally, an augmented graph is a pair (G,ψ) where G is a graph, and ψ is a collection of probability distributions {ψu, u ∈ V(G)}. Every node u ∈ V(G) is given an extra link, called a long range link, pointing to some node v, called the long range contact of u. The head v of this link is chosen at random by Pr{u → v} = ψu(v). In augmented graphs, greedy routing is the oblivious routing process in which every intermediate node chooses among all its neighbors (including its long range contact) the one that is closest to the target according to the distance measured in the underlying graph G, and forwards to it. Roughly, augmented graphs aim at modeling the structure of social networks, while greedy routing aims at modeling the searching procedure applied in Milgram's experiment. Our objective is to design efficient universal augmentation schemes, i.e., augmentation schemes that give to any graph G a collection of probability distributions ψ such that greedy routing in (G,ψ) is fast. It is known that the uniform scheme ψunif is a universal scheme ensuring that, for any n-node graph G, greedy routing in (G,ψunif) performs in O(√n) expected number of steps. Our main result is the design of a universal augmentation scheme ψ such that greedy routing in (G,ψ) performs in Õ(n1/3) expected number of steps for any n-node graph G. We also show that under some more restricted model, the √n-barrier cannot be overcome.

    Original languageEnglish
    Title of host publicationSPAA'07
    Subtitle of host publicationProceedings of the Nineteenth Annual Symposium on Parallelism in Algorithms and Architectures
    Pages1-7
    Number of pages7
    DOIs
    StatePublished - 18 Oct 2007
    EventSPAA'07: 19th Annual Symposium on Parallelism in Algorithms and Architectures - San Diego, CA, United States
    Duration: 9 Jun 200711 Jun 2007

    Publication series

    NameAnnual ACM Symposium on Parallelism in Algorithms and Architectures

    Conference

    ConferenceSPAA'07: 19th Annual Symposium on Parallelism in Algorithms and Architectures
    Country/TerritoryUnited States
    CitySan Diego, CA
    Period9/06/0711/06/07

    Keywords

    • Small world phenomenon

    ASJC Scopus subject areas

    • General Engineering

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