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A Tight Bound for β-Skeleton of Minimum Weight Triangulations

  • Cao An Wang
  • Boting Yang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1663)

Abstract

In this paper, we prove a tight bound for β value \( \left( {\beta = \frac{{\sqrt {2\sqrt 3 + 9} }} {3}} \right) \) ) such that being less than this value,the β-skeleton of a planar point set may not belong to the minimum weight triangulation of this set, while being equal to or greater than this value, the β-skeleton always belongs to the minimum weight triangulation. Thus, we settled the conjecture of the tight bound for β-skeleton of minimum weight triangulation by Mark Keil. We also present a new sufficient condition for identifying a subgraph of minimum weight triangulation of a planar n-point set. The identified subgraph could be different from all the known subgraphs, and the subgraph can be found in O(n 2 log n) time.

Keywords

Line Segment Convex Hull Computational Geometry Internal Edge Primal Plane 
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

  • Cao An Wang
    • 1
  • Boting Yang
    • 1
  1. 1.Department of Computer ScienceMemorial University of NewfoundlandSt.John’s, NFLDCanada

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