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On parallel complexity of planar triangulations

  • Computational Geometry
  • Conference paper
  • First Online:
Foundations of Software Technology and Theoretical Computer Science (FSTTCS 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1026))

Abstract

The greedy triangulation of a finite planar point set is obtained by repeatedly inserting a shortest diagonal that doesn't intersect those already in the plane. We show that the problem of constructing the greedy triangulation of a finite set of points with integer coordinates in the plane is P-complete. This is the first known geometric P-complete problem where the input is given as a set of points. On the other hand, we provide general NC-methods for testing whether a given triangulation of a set of points and/or line segments can be built by inserting the diagonals in a given partial order, and for constructing such triangulations for simple polygons. As corollaries, we obtain NC-algorithms for testing whether a triangulation is respectively the greedy triangulation or the so called sweep-line triangulation, and for constructing respectively the greedy triangulation or the sweep-line triangulation of a simple polygon. The latter result solves the open problem posed by Atallah et al.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Lund University, Box 118, S-221 00, Lund, Sweden

    Christos Levcopoulos & Andrzej Lingas

  2. Department of Computer Science, Memorial University of Newfoundland, A1C 5S7, St. John's, Canada

    Cao Wang

Authors
  1. Christos Levcopoulos
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  2. Andrzej Lingas
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  3. Cao Wang
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Editor information

P. S. Thiagarajan

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© 1995 Springer-Verlag Berlin Heidelberg

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Levcopoulos, C., Lingas, A., Wang, C. (1995). On parallel complexity of planar triangulations. In: Thiagarajan, P.S. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1995. Lecture Notes in Computer Science, vol 1026. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60692-0_64

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  • DOI: https://doi.org/10.1007/3-540-60692-0_64

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60692-5

  • Online ISBN: 978-3-540-49263-4

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