A nearly optimal parallel algorithm for the voronoi diagram of a convex polygon

Piotr Berman, Andrzej Lingas

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

    Abstract

    We present a parMlel algorithm for the Voronoi diagram of the set of vertices of a convex polygon. The algorithm runs in time O(log n) and uses O(nloglog n/log n) processors in the CRCW PRAM model. The concurrent write is used only by an integer sorting subroutine. We also obtain an O(log n)-time and O(n log log n log n)-proceor CRCW PRAM algorithm for the construction of the medial axis of a convex polygon. Our algorithms use the solution to the duration-unknown task scheduling problem due to Cole and Vishkin and the optimal parallel algorithm for the convex hull of a polygon due to Wagener. They are randomized in the sense that for any given I > 0 they terminate in time O(log n) with probability greater than 1-n -1.

    Original languageEnglish (US)
    Title of host publicationAlgorithm Theory – SWAT 1994 - 4th Scandinavian Workshop on Algorithm Theory, Proceedings
    EditorsErik M. Schmidt, Sven Skyum
    PublisherSpringer Verlag
    Pages73-82
    Number of pages10
    ISBN (Print)9783540582182
    DOIs
    StatePublished - 1994
    Event4th Scandinavian Workshop on Algorithm Theory, SWAT 1994 - Aarhus, Denmark
    Duration: Jul 6 1994Jul 8 1994

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume824 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other4th Scandinavian Workshop on Algorithm Theory, SWAT 1994
    CountryDenmark
    CityAarhus
    Period7/6/947/8/94

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

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  • Cite this

    Berman, P., & Lingas, A. (1994). A nearly optimal parallel algorithm for the voronoi diagram of a convex polygon. In E. M. Schmidt, & S. Skyum (Eds.), Algorithm Theory – SWAT 1994 - 4th Scandinavian Workshop on Algorithm Theory, Proceedings (pp. 73-82). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 824 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-58218-5_7