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Minimum Weight Pseudo-Triangulations

(Extended Abstract)
  • Joachim Gudmundsson
  • Christos Levcopoulos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3328)

Abstract

We consider the problem of computing a minimum weight pseudo-triangulation of a set \({\mathcal S}\) of n points in the plane. We first present an \(\mathcal O(n {\rm log} n)\)-time algorithm that produces a pseudo-triangulation of weight \(O(wt(\mathcal M(\mathcal S)).{\rm log} n)\) which is shown to be asymptotically worst-case optimal, i.e., there exists a point set \({\mathcal S}\) for which every pseudo-triangulation has weight \(\Omega({\rm log} n.wt(\mathcal M(\mathcal S))\), where \(wt(\mathcal M(\mathcal S))\) is the weight of a minimum spanning tree of \({\mathcal S}\). We also present a constant factor approximation algorithm running in cubic time. In the process we give an algorithm that produces a minimum weight pseudo-triangulation of a simple polygon.

Keywords

Convex Hull Minimum Span Tree Minimum Weight Steiner Point 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 2004

Authors and Affiliations

  • Joachim Gudmundsson
    • 1
  • Christos Levcopoulos
    • 2
  1. 1.Department of Mathematics and Computing ScienceTU EindhovenEindhovenThe Netherlands
  2. 2.Department of Computer ScienceLund UniversityLundSweden

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