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A Parallel Algorithm for Finding the Constrained Voronoi Diagram of Line Segments in the Plane

  • Fancis Chin
  • Derz Tsai Lee
  • Cao An Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1663)

Abstract

In this paper, we present an O \( O\left( {\frac{1} {\alpha }\log n} \right) \) log n) (for any constant 0 ≤α≤1) time parallel algorithm for constructing the constrained Voronoi diagram of a set L of n non-crossing line segments in E 2, using O(n 1+α) processors on a CREW PRAM model. This parallel algorithm also constructs the constrained Delaunay triangulation of L in the same time and processor bound by the duality.

Our method established the conversions from finding the constrained Voronoi diagram L to finding the Voronoi diagram of S, the endpoint set of L. We further showed that this conversion can be done in O(log n) time using n processors in CREW PRAM model. The complexity of the conversion implies that any improvement of the complexity for finding the Voronoi diagram of a point set will automatically bring the improvement of the one in question.

Keywords

Convex Hull Parallel Algorithm Voronoi Diagram Delaunay Triangulation Voronoi Cell 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Fancis Chin
    • 1
  • Derz Tsai Lee
    • 2
  • Cao An Wang
    • 3
  1. 1.Department of CSISUniversity of Hong KongHong Kong
  2. 2.Department of ECENorthwestern UniversityEvanstonUSA
  3. 3.Department of Computer ScienceMemorial University of NewfoundlandSt.John’s, NFLDCanada

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