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Plane-Sweep Algorithm of O(nlogn) for the Inclusion Hierarchy among Circles

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Computational Science and Its Applications – ICCSA 2004 (ICCSA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3045))

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Abstract

Suppose that we have a number of circles in a plane and some of them may contain other circles. Then, finding the hierarchy among circles is of important for various applications such as the simulation of emulsion. In this paper, we present a standard plane-sweep algorithm which can identify the inclusion relationship among the circles in O(nlogn) time in the worst-case. The algorithm uses a number of sweep-lines and a red-black tree for the efficient computation.

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Author information

Authors and Affiliations

  1. Department of Industrial Engineering, Hanyang University, 17 Haengdang-Dong, Sungdong-Ku, Seoul, 133-791, South Korea

    Deok-Soo Kim, Byunghoon Lee & Cheol-Hyung Cho

  2. Department of Mathematical Informatics, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo, 113-8685, Japan

    Kokichi Sugihara

Authors
  1. Deok-Soo Kim
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  2. Byunghoon Lee
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  3. Cheol-Hyung Cho
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  4. Kokichi Sugihara
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Editor information

Editors and Affiliations

  1. Department of Chemistry, University of Perugia, Via Elce di Sotto, 8, I-06123, Perugia, Italy

    Antonio Laganá

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  3. William Norris Professor, Head of the Computer Science and Engineering Department, University of Minnesota, USA

    Vipin Kumar

  4. School of Computing, Soongsil University, Seoul, Korea

    Youngsong Mun

  5. OptimaNumerics Ltd., Cathedral House, 23-31 Waring Street, BT1 2DX, Belfast, UK

    C. J. Kenneth Tan

  6. Department of Mathematics and Computer Science, University of Perugia, via Vanvitelli, 1, I-06123, Perugia, Italy

    Osvaldo Gervasi

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© 2004 Springer-Verlag Berlin Heidelberg

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Kim, DS., Lee, B., Cho, CH., Sugihara, K. (2004). Plane-Sweep Algorithm of O(nlogn) for the Inclusion Hierarchy among Circles. In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds) Computational Science and Its Applications – ICCSA 2004. ICCSA 2004. Lecture Notes in Computer Science, vol 3045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24767-8_6

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  • DOI: https://doi.org/10.1007/978-3-540-24767-8_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22057-2

  • Online ISBN: 978-3-540-24767-8

  • eBook Packages: Springer Book Archive

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