Approximate distance queries in disk graphs

Martin Furer, Shiva Prasad Kasiviswanathan

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

    1 Scopus citations

    Abstract

    We present efficient algorithms for approximately answering distance queries in disk graphs. Let G be a disk graph with n vertices and m edges. For any fixed ε > 0, we show that G can be preprocessed in O(m√nε-1 + mε-2 log S) time, constructing a data structure of size O(n3/2ε-1 + nε-2 log S), such that any subsequent distance query can be answered approximately in O(√nε-1-2log S) time. Here S is the ratio between the largest and smallest radius. The estimate produced is within an additive error which is only e times the longest edge on some shortest path. The algorithm uses an efficient subdivision of the plane to construct a sparse graph having many of the same distance properties as the input disk graph. Additionally, the sparse graph has a small separator decomposition, which is then used to answer distance queries. The algorithm extends naturally to the higher dimensional ball graphs.

    Original languageEnglish (US)
    Title of host publicationApproximation and Online Algorithms - 4th International Workshop, WAOA 2006, Revised Papers
    Pages174-187
    Number of pages14
    Publication statusPublished - Dec 1 2007
    Event4th Workshop on Approximation and Online Algorithms, WAOA 2006 - Zurich, Switzerland
    Duration: Sep 14 2006Sep 15 2006

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume4368 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other4th Workshop on Approximation and Online Algorithms, WAOA 2006
    CountrySwitzerland
    CityZurich
    Period9/14/069/15/06

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    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Furer, M., & Kasiviswanathan, S. P. (2007). Approximate distance queries in disk graphs. In Approximation and Online Algorithms - 4th International Workshop, WAOA 2006, Revised Papers (pp. 174-187). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4368 LNCS).