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Efficient Computation of Elliptic Gabriel Graph

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Computational Science and Its Applications - ICCSA 2006 (ICCSA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3980))

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Abstract

Searching neighboring points around a point in a point set has been important for various applications and there have been extensive studies such as the minimum spanning tree, relative neighborhood graph, Delaunay triangulation, Gabriel graph, and so on.

Observing the fact that the previous approaches of neighbor search may possibly sample severely biased neighbors in a set of unevenly distributed points, an elliptic Gabriel graph has recently been proposed. By extending the influence region from a circle to an ellipse, the elliptic Gabriel graph generalizes the ordinary Gabriel graph. Hence, the skewness in the sampled neighbors is rather reduced.

In this paper, we present a simple observation which allows to compute the correct elliptic Gabriel graph efficiently by reducing the search space.

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Author information

Authors and Affiliations

  1. Dept. of Industrial Engineering, Hanyang University, Seoul, Korea

    Changhee Lee, Donguk Kim & Deok-Soo Kim

  2. Dept. of Industrial Engineering, KAIST, Daejeon, Korea

    Hayong Shin

Authors
  1. Changhee Lee
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  2. Donguk Kim
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  3. Hayong Shin
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  4. Deok-Soo Kim
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Editor information

Editors and Affiliations

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

    Marina Gavrilova

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

    Osvaldo Gervasi

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

    Vipin Kumar

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

    C. J. Kenneth Tan

  5. Clayton School of IT, Monash University, 3800, Clayton, Australia

    David Taniar

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

    Antonio Laganá

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

    Youngsong Mun

  8. School of Information and Communication Engineering, Sungkyunkwan University, Korea

    Hyunseung Choo

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© 2006 Springer-Verlag Berlin Heidelberg

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Lee, C., Kim, D., Shin, H., Kim, DS. (2006). Efficient Computation of Elliptic Gabriel Graph. In: Gavrilova, M., et al. Computational Science and Its Applications - ICCSA 2006. ICCSA 2006. Lecture Notes in Computer Science, vol 3980. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11751540_47

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  • DOI: https://doi.org/10.1007/11751540_47

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34070-6

  • Online ISBN: 978-3-540-34071-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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