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On Convex Decompositions of Points

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Book cover Discrete and Computational Geometry (JCDCG 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2098))

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Abstract

Given a planaler point set in general position, S, we seek a partition of the points into convex cells, such that the union of the cells forms a simple polygon, P, and every point from S is on the boundary of P. Let f(S) denote the minimum number of cells in such a partition of S. Let F(n) be defined as the maximum value of f(S) when S has n points. In this paper we show that ⌈(n - 1)/4⌉ ≤ F(n) ≤ ⌊(3n - 2)/5⌋ .

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Tokai University, 3-20-1, Orido, Shimizu, Shizuoka, 424-8610, Japan

    Kiyoshi Hosono & Masatsugu Urabe

  2. Department of Computing and Information Science, Queen’s University, Kingston, Ontario, K7L 3N6, Canada

    David Rappaport

Authors
  1. Kiyoshi Hosono
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  2. David Rappaport
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  3. Masatsugu Urabe
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Editor information

Editors and Affiliations

  1. Research Institute of Educational Development, Tokai University, 2-28-4 Tomigaya, Shibuya-ku, Tokyo, 151-0063, Japan

    Jin Akiyama

  2. Department of Computer and Information Sciences, Ibaraki University, Hitachi, 316-8511, Japan

    Mikio Kano

  3. Department of Mathematics, Tokai University, 3-20-1 Orido Shimizu-shi, Shizuoka, 424-8610, Japan

    Masatsugu Urabe

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© 2001 Springer-Verlag Berlin Heidelberg

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Hosono, K., Rappaport, D., Urabe, M. (2001). On Convex Decompositions of Points. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol 2098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47738-1_12

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  • DOI: https://doi.org/10.1007/3-540-47738-1_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42306-5

  • Online ISBN: 978-3-540-47738-9

  • eBook Packages: Springer Book Archive

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