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Constrained independence system and triangulations of planar point sets

  • Siu-Wing Chengl
  • Yin-Feng Xu
Session 2A: Computational Geometry
Part of the Lecture Notes in Computer Science book series (LNCS, volume 959)

Abstract

We propose and study a new constrained independence system. We obtain a sequence of results, including a matching theorem for bases of the system and introducing a set of light elements which give a lower bound for the objective function of a minimization problem in the system. We then demonstrate that the set of triangulations of a planar point set can be modeled as constrained independence systems. The corresponding minimization problem in the system is the well-known minimum weight triangulation problem. Thus, we obtain two matching theorems for triangulations and a set of light edges (or light triangles) that give a lower bound for the minimum weight triangulation. We also prove directly a third matching theorem for triangulations. We show that the set of light edges is a superset of some subsets of edges of a minimum weight triangulation that were studied before.

Keywords

Minimization Problem Bipartite Graph Perfect Match Algorithm Greedy Greedy Solution 
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 1995

Authors and Affiliations

  • Siu-Wing Chengl
    • 1
  • Yin-Feng Xu
    • 2
  1. 1.Department of Computer ScienceThe Hong Kong University of Science & TechnologyClear Water BayHong Kong
  2. 2.School of ManagementXi'an Jiaotong UniversityXi'an, ShaanxiPRC

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