Spanners for geometric intersection graphs

Martin Fürer, Shiva Prasad Kasiviswanathan

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    5 Scopus citations

    Abstract

    A disk graph is an intersection graph of a set of disks with arbitrary radii in the plane. In this paper, we consider the problem of efficient construction of sparse spanners of disk (ball) graphs with support for fast distance queries. These problems are motivated by issues arising from topology control and routing in wireless networks. We present the first algorithm for constructing spanners of ball graphs. For a ball graph in ℝk, we construct a (1 + ε)-spanner with O(nε-k+1) edges in O(n2ℓ+εε-k log S) expected time, using an efficient partitioning of the space into hypercubes and solving intersection problems. Here ℓ = 1-1/(⌊k/2⌋+2), ε is any positive constant, and S is the ratio between the largest and smallest radius. For the special case where all the balls have the same radius, we show that the spanner construction has complexity almost equivalent to the construction of a Euclidean minimum spanning tree. Previously known constructions of spanners of unit ball graphs have time complexity much closer to n2. Additionally, these spanners have a small vertex separator (hereditary), which is then exploited for fast answering of distance queries. The results on geometric graph separators might be of independent interest.

    Original languageEnglish (US)
    Title of host publicationAlgorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings
    PublisherSpringer Verlag
    Pages312-324
    Number of pages13
    ISBN (Print)3540739483, 9783540739487
    DOIs
    StatePublished - 2007
    Event10th International Workshop on Algorithms and Data Structures, WADS 2007 - Halifax, Canada
    Duration: Aug 15 2007Aug 17 2007

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume4619 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other10th International Workshop on Algorithms and Data Structures, WADS 2007
    CountryCanada
    CityHalifax
    Period8/15/078/17/07

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

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