On Geometric Algorithms that use the Furthest-Point Voronoi Diagram

Binay K. Bhattacharya, Godfried Toussaint

    Research output: Contribution to journalArticle

    Abstract

    In this paper it is shown that the diameter D(P) of a set of n points P on the plane is not necessarily an edge in the dual of the furthest-point Voronoi diagram (FPVD) of P, as previously claimed in [1] and [2]. It is also proved that if P is contained in the disk determined by D(P) then the above property does hold. Furthermore, it is shown that an edge e in the dual of the FPVD(P) intersects its corresponding edge in the FPVD(P) if, and only if, P is contained in the disk determined by e. These results invalidate several algorithms for solving the diameter, all-furthest-neighbor, and maximal spanning tree problems proposed in [1] and [2]. A proof of correctness is given for the minimum spanning circle algorithm proposed in [2] and [3]. Finally new O(n log n) algorithms are offered for the minimum spanning circle and all-furthest-neighbor problems.

    Original languageEnglish (US)
    Pages (from-to)43-61
    Number of pages19
    JournalMachine Intelligence and Pattern Recognition
    Volume2
    Issue numberC
    DOIs
    StatePublished - Jan 1 1985

    Keywords

    • 3.36
    • 3.63
    • 5.25
    • 5.30
    • 5.5
    • algorithms
    • all-furthest-neighbor problem
    • computational geometry
    • convex hull
    • diameter
    • maximal spanning tree
    • minimum spanning circle
    • Voronoi diagram

    ASJC Scopus subject areas

    • Computer Vision and Pattern Recognition
    • Artificial Intelligence

    Cite this

    On Geometric Algorithms that use the Furthest-Point Voronoi Diagram. / Bhattacharya, Binay K.; Toussaint, Godfried.

    In: Machine Intelligence and Pattern Recognition, Vol. 2, No. C, 01.01.1985, p. 43-61.

    Research output: Contribution to journalArticle

    Bhattacharya, Binay K. ; Toussaint, Godfried. / On Geometric Algorithms that use the Furthest-Point Voronoi Diagram. In: Machine Intelligence and Pattern Recognition. 1985 ; Vol. 2, No. C. pp. 43-61.
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