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A chain decomposition algorithm for the proof of a property on minimum weight triangulations

  • Yang Bo-Ting
  • Xu Yin-Feng
  • You Zhao-Yong
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 834)

Abstract

In this paper, a chain decomposition algorithm is proposed and studied. Using this algorithm, we prove a property on minimum weight triangulations of points in the Euclidean plane, which shows that a special kind of line segments must be in the minimum weight triangulations and in the greedy triangulation of a given point set.

Keywords

Chain algorithm triangulation computational geometry 

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References

  1. [1]
    L. S. Heath and S. V. Pemmaraju, New results for the minimum weight triangulation problem, TR 90-65, Virginia Polytechnic Institute and state University, 1990.Google Scholar
  2. [2]
    A. Lingas, A new heuristic for the minimum weight triangulation, SIAM Journal of Algebraic and Discrete Methods 8, 646–658. 1987.Google Scholar
  3. [3]
    Y. F. Xu, Minimum Weight trianuglation problem of a planar point set, ph. D. thesis, Institute of Applied Mathematics, Academia Sinica, Beiing, 1992.Google Scholar
  4. [4]
    F. Preparata and M. I. Shamos. Computational Geometry, Springer-Verlag, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Yang Bo-Ting
    • 1
  • Xu Yin-Feng
    • 1
  • You Zhao-Yong
    • 1
  1. 1.Institute for Computational and Applied MathematicsXi'an Jiaotong UniversityChina

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