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A new subgraph of minimum weight triangulations

  • Session 7a: Invited Presentation
  • Conference paper
  • First Online:
Algorithms and Computation (ISAAC 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1178))

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Abstract

In this paper, two sufficient conditions for identifying a subgraph of minimum weight triangulation of a planar point set are presented. These conditions are based on local geometric properties of an identifying edge in the given point set. Unlike the previous known sufficient conditions for identifying subgraphs, such as Keil's β-skeleton and Yang and Xu's double circles, The local geometric requirement in our conditions is not necessary symmetric with respect to the edge to be identified. The identified subgraph is different from all the known subgraphs including the newly discovered subgraph: so-called the intersection of local-optimal triangulations by Dickerson, Montague, and Keil. An O(n 3) time algorithm for finding this subgraph from a set of n points is presented.

This work is partially supported by NSERC grant OPG0041629 and HKU funded project HKU 287/95E through RGC firect allocation.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Memorial University of Newfoundland, A1C 5S7, St.John's, NFLD, Canada

    Cao An Wang

  2. Department of Computer Science, University of Hong Kong, Hong Kong

    Francis Chin

  3. The school of management, Xi'an Jiaotong University, 710049, Xi'an, P.R. China

    Yin-Feng Xu

Authors
  1. Cao An Wang
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  2. Francis Chin
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  3. Yin-Feng Xu
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Editor information

Tetsuo Asano Yoshihide Igarashi Hiroshi Nagamochi Satoru Miyano Subhash Suri

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© 1996 Springer-Verlag Berlin Heidelberg

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Wang, C.A., Chin, F., Xu, YF. (1996). A new subgraph of minimum weight triangulations. In: Asano, T., Igarashi, Y., Nagamochi, H., Miyano, S., Suri, S. (eds) Algorithms and Computation. ISAAC 1996. Lecture Notes in Computer Science, vol 1178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0009503

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  • DOI: https://doi.org/10.1007/BFb0009503

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62048-8

  • Online ISBN: 978-3-540-49633-5

  • eBook Packages: Springer Book Archive

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