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Optimal Direction for Monotone Chain Decomposition

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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 3044))

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Abstract

Monotone chain is an important concept in computational geometry. A general polygon or polygonal chain can be decomposed into monotone chains. Described in this paper are two algorithms to find an optimal direction with respect to which a polygonal chain can be split into the minimal number of monotone chains. The first naive algorithm has O(n 2) time complexity, while the improved algorithm runs in O(n log n) time, where n is the number of vertices of input chain. The optimal direction can improve the performance of the subsequent geometric processing.

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Author information

Authors and Affiliations

  1. KAIST, Dept. of Industrial Engineering, S. Korea

    Hayong Shin

  2. Dept. of Industrial Engineering, Hanyang Univ., S. Korea

    Deok-Soo Kim

Authors
  1. Hayong Shin
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  2. Deok-Soo Kim
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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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Shin, H., Kim, DS. (2004). Optimal Direction for Monotone Chain Decomposition. 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 3044. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24709-8_62

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  • DOI: https://doi.org/10.1007/978-3-540-24709-8_62

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22056-5

  • Online ISBN: 978-3-540-24709-8

  • eBook Packages: Springer Book Archive

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