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A sweep-line algorithm for the inclusion hierarchy among circles

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Abstract

Suppose that there are a number of circles in a plane and some of them may contain several smaller circles. In this case, it is necessary to find the inclusion hierarchy among circles for the various applications such as the simulation of emulsion and diameter estimation for wire bundles. In this paper, we present a plane-sweep algorithm that can identify the inclusion hierarchy among the circles inO(n logn) time in the worst-case. Also, the proposed algorithm uses the sweep-line method 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, Seongdong-gu, 133-791, Seoul, Korea

    Deok-Soo Kim

  2. Voronoi Diagram Research Center, Department of Industrial Engineering, Hanyang University, 17 Haengdang-dong, Seongdong-gu, 133-791, Seoul, Korea

    Byunghoon Lee

  3. Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, 113-8656, Tokyo, Japan

    Kokichi Sugihara

Authors
  1. Deok-Soo Kim
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  2. Byunghoon Lee
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  3. Kokichi Sugihara
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Correspondence to Deok-Soo Kim.

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Kim, DS., Lee, B. & Sugihara, K. A sweep-line algorithm for the inclusion hierarchy among circles. Japan J. Indust. Appl. Math. 23, 127 (2006). https://doi.org/10.1007/BF03167502

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  • DOI: https://doi.org/10.1007/BF03167502

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