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

Piotr Berman, Andrzej Lingas

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    We present a parallel 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(n log log 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)-processor 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 l > 0 they terminate in time O(log n) with probability greater than 1 - n-1.

    Original languageEnglish (US)
    Pages (from-to)193-202
    Number of pages10
    JournalTheoretical Computer Science
    Volume174
    Issue number1-2
    DOIs
    StatePublished - Mar 15 1997

    Fingerprint

    Convex polygon
    Voronoi Diagram
    Optimal Algorithm
    Parallel algorithms
    Parallel Algorithms
    Medial Axis
    Task Scheduling
    Subroutines
    Terminate
    Sorting
    Convex Hull
    Polygon
    Scheduling Problem
    Concurrent
    Scheduling
    Unknown
    Integer
    Model

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Berman, Piotr ; Lingas, Andrzej. / A nearly optimal parallel algorithm for the Voronoi diagram of a convex polygon. In: Theoretical Computer Science. 1997 ; Vol. 174, No. 1-2. pp. 193-202.
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    A nearly optimal parallel algorithm for the Voronoi diagram of a convex polygon. / Berman, Piotr; Lingas, Andrzej.

    In: Theoretical Computer Science, Vol. 174, No. 1-2, 15.03.1997, p. 193-202.

    Research output: Contribution to journalArticle

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