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A New Subgraph of Minimum Weight Triangulations

Author

Listed:
  • Cao An Wang

    (Memorial University of Newfoundland)

  • Francis Chin

    (University of Hong Kong)

  • Yin-Feng Xu

    (Xi‘an Jiaotong University)

Abstract

In this paper, two sufficient conditions for identifying a subgraph ofminimum weight triangulation of a planar point set are presented. Theseconditions are based on local geometric properties of an edge to beidentified. Unlike the previous known sufficient conditions for identifyingsubgraphs, such as Keil‘sβ-skeleton and Yang and Xu‘s double circles, The localgeometric requirement in our conditions is not necessary symmetric withrespect to the edge to be identified. The identified subgraph is differentfrom all the known subgraphs including the newly discovered subgraph:so-called the intersection of local-optimal triangulations by Dickerson etal. An O(n3) time algorithm for finding this subgraph from a set ofn points is presented.

Suggested Citation

  • Cao An Wang & Francis Chin & Yin-Feng Xu, 1997. "A New Subgraph of Minimum Weight Triangulations," Journal of Combinatorial Optimization, Springer, vol. 1(2), pages 115-127, June.
    • Handle: RePEc:spr:jcomop:v:1:y:1997:i:2:d:10.1023_a:1009796113861
    DOI: 10.1023/A:1009796113861
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    Cited by:

    1. Shiyan Hu, 2010. "A new asymmetric inclusion region for minimum weight triangulation," Journal of Global Optimization, Springer, vol. 46(1), pages 63-73, January.

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