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International Conference on Foundations of Software Technology and Theoretical Computer Science

FSTTCS 1992: Foundations of Software Technology and Theoretical Computer Science pp 104–115Cite as

C-sensitive triangulations approximate the minmax length triangulation

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 652))

Abstract

We introduce the notion of a c-sensitive triangulation based on the local notion of a c-sensitive triangulation edge. We show that any c-sensitive triangulation of a planar point set approximates the minmax length triangulation of the set within the factor 2(c+1). On the other hand we prove that the greedy triangulation and the Dclaunay triangulation of a planar straight-line graph are respectively 4-sensitive and 1-sensitive. We also generalize the relationship between c-sensitive triangulations and the minmax length triangulation to include appropriately augmented planar straight-line graphs. This enables us to obtain a O(n) log n)-time heuristic for the minmax length triangulation of an arbitrary planar straight-line graph with the approximation factor bounded by 3. A modification of the above heuristic for simple polygons runs in linear time.

This work was partially supported by NFR, STU, STUF and TFR.

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Authors and Affiliations

  1. Department of Computer Science, Lund University, Box 118, S-221 00, Lund, Sweden

    Christos Levcopoulos & Andrzej Lingas

Authors
  1. Christos Levcopoulos
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  2. Andrzej Lingas
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Editor information

Rudrapatna Shyamasundar

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© 1992 Springer-Verlag Berlin Heidelberg

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Levcopoulos, C., Lingas, A. (1992). C-sensitive triangulations approximate the minmax length triangulation. In: Shyamasundar, R. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1992. Lecture Notes in Computer Science, vol 652. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56287-7_98

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  • DOI: https://doi.org/10.1007/3-540-56287-7_98

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56287-0

  • Online ISBN: 978-3-540-47507-1

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