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A Parallel Approximation Algorithm for Minimum Weight Triangulation

  • Joachim Gudmundsson
  • Christos Levcopoulos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1530)

Abstract

We show a parallel algorithm that produces a triangulation which is within a constant factor longer than the Minimum Weight Triangulation (MWT) in time O(logn) using O(n) processors and linear space in the CRCW PRAM model. This is done by developing a relaxed version of the quasi-greedy triangulation algorithm. The relaxed version produces edges that are at most (1+ε) longer than the shortest diagonal, where ε is some positive constant smaller than 1, still outputs a triangulation which is within a constant factor longer that the minimum weight triangulation. However, if the same method is applied to the straight-forward greedy algorithm the approximation behavior may deteriorate dramatically, i.e. Ω(n) longer than a minimum weight triangulation, if the lengths of the edges are not computed with high precision.

Keywords

Convex Hull Greedy Algorithm Delaunay Triangulation Convex Polygon Simple Polygon 
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 1998

Authors and Affiliations

  • Joachim Gudmundsson
    • 1
  • Christos Levcopoulos
    • 1
  1. 1.Department of Computer ScienceLund UniversityLundSweden

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