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)


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.


Convex Hull Minimum Span Tree Minimum Weight Steiner Point Simple Polygon 
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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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