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International Symposium on Algorithms and Computation

ISAAC 1997: Algorithms and Computation pp 384–393Cite as

A branch-and-cut approach for minimum weight triangulation

  • Session 8A
  • Conference paper
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1350))

Abstract

This paper considers the problem of computing a minimum weight triangulation of n points in the plane, which has been intensively studied in recent years in computational geometry. This paper investigates a branch-and-cut approach for minimum weight triangulations. The problem can be formulated as finding a minimum-weight maximal independent set of intersection graphs of edges. In combinatorial optimization, there are known many cuts for the independent set problem, and we further use a cut induced by geometric properties of triangulations. Combining this branch-and-cut approach with the β-skeleton method, the moderate-size problem could be solved efficiently in our computational experiments. Polyhedral characterizations of the proposed cut and applications of another old skeletal approach in mathematical programming as the independent set problem are also touched upon.

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Author information

Authors and Affiliations

  1. Department of Information Science, University of Tokyo, Japan

    Yoshiaki Kyoda & Fumihiko Takeuchi

  2. Department of Information and System Engineering, Chuo University, Japan

    Keiko Imai

  3. IBM Tokyo Research Laboratory, Japan

    Akira Tajima

Authors
  1. Yoshiaki Kyoda
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  2. Keiko Imai
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  3. Fumihiko Takeuchi
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  4. Akira Tajima
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Editor information

Hon Wai Leong Hiroshi Imai Sanjay Jain

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© 1997 Springer-Verlag Berlin Heidelberg

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Kyoda, Y., Imai, K., Takeuchi, F., Tajima, A. (1997). A branch-and-cut approach for minimum weight triangulation. In: Leong, H.W., Imai, H., Jain, S. (eds) Algorithms and Computation. ISAAC 1997. Lecture Notes in Computer Science, vol 1350. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63890-3_41

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  • DOI: https://doi.org/10.1007/3-540-63890-3_41

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63890-2

  • Online ISBN: 978-3-540-69662-9

  • eBook Packages: Springer Book Archive

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