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Discrete & Computational Geometry

, Volume 16, Issue 4, pp 339–359 | Cite as

Triangulations intersect nicely

  • O. Aichholzer
  • F. Aurenhammer
  • Siu-Wing Cheng
  • N. Katoh
  • G. Rote
  • M. Taschwer
  • Yin-Feng Xu
Article

Abstract

We show that there is a matching between the edges of any two triangulations of a planar point set such that an edge of one triangulation is matched either to the identical edge in the other triangulation or to an edge that crosses it. This theorem also holds for the triangles of the triangulations and in general independence systems. As an application, we give some lower bounds for the minimum-weight triangulation which can be computed in polynomial time by matching and network-flow techniques. We exhibit an easy-to-recognize class of point sets for which the minimum-weight triangulation coincides with the greedy triangulation.

Keywords

Bipartite Graph Short Edge Adjacency List Identical Edge Planar Triangulation 
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 New York Inc 1996

Authors and Affiliations

  • O. Aichholzer
    • 1
  • F. Aurenhammer
    • 1
  • Siu-Wing Cheng
    • 2
  • N. Katoh
    • 3
  • G. Rote
    • 4
  • M. Taschwer
    • 1
  • Yin-Feng Xu
    • 5
  1. 1.Institute for Theoretical Computer ScienceGraz University of TechnologyGrazAustria
  2. 2.Department of Computer ScienceHong Kong University of Science and TechnologyClear Water BayHong Kong
  3. 3.Department of Management ScienceKobe University of CommerceKobeJapan
  4. 4.Institut für MathematikTechnische Universität GrazGrazAustria
  5. 5.School of ManagementXi'an Jiaotong UniversityXi'an ShaanxiPeople's Republic of China

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