On computing the centroid of the vertices of an arrangement and related problems

Deepak Ajwani, Saurabh Ray, Raimund Seidel, Hans Raj Tiwary

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

    Abstract

    We consider the problem of computing the centroid of all the vertices in a non-degenerate arrangement of n lines. The trivial approach requires the enumeration of all (n/2) vertices. We present an O(n log2 n) algorithm for computing this centroid. For arrangements of n segments we give an O(n4/3+ε) algorithm for computing the centroid of its vertices. For the special case that all the segments of the arrangement are chords of a simply connected planar region we achieve an O(n log5 n) time bound. Our bounds also generalize to certain natural weighted versions of those problems.

    Original languageEnglish (US)
    Title of host publicationAlgorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings
    Pages519-528
    Number of pages10
    StatePublished - Dec 1 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

    Fingerprint

    Centroid
    Arrangement
    Computing
    Chord or secant line
    Enumeration
    Trivial
    Generalise
    Line

    ASJC Scopus subject areas

    • Computer Science(all)
    • Biochemistry, Genetics and Molecular Biology(all)
    • Theoretical Computer Science

    Cite this

    Ajwani, D., Ray, S., Seidel, R., & Tiwary, H. R. (2007). On computing the centroid of the vertices of an arrangement and related problems. In Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings (pp. 519-528). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4619 LNCS).

    On computing the centroid of the vertices of an arrangement and related problems. / Ajwani, Deepak; Ray, Saurabh; Seidel, Raimund; Tiwary, Hans Raj.

    Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings. 2007. p. 519-528 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4619 LNCS).

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

    Ajwani, D, Ray, S, Seidel, R & Tiwary, HR 2007, On computing the centroid of the vertices of an arrangement and related problems. in Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4619 LNCS, pp. 519-528, 10th International Workshop on Algorithms and Data Structures, WADS 2007, Halifax, Canada, 8/15/07.
    Ajwani D, Ray S, Seidel R, Tiwary HR. On computing the centroid of the vertices of an arrangement and related problems. In Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings. 2007. p. 519-528. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
    Ajwani, Deepak ; Ray, Saurabh ; Seidel, Raimund ; Tiwary, Hans Raj. / On computing the centroid of the vertices of an arrangement and related problems. Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings. 2007. pp. 519-528 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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