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Area Bounds of Rectilinear Polygons Realized by Angle Sequences

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Algorithms and Computation (ISAAC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7676))

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Abstract

Given a sequence S of angles at n vertices of a rectilinear polygon, S directly defines (or realizes) a set of rectilinear polygons in the integer grid. Among such realizations, we consider the one P(S) with minimum area. Let δ(n) be the minimum of the area of P(S) over all angle sequences S of length n, and Δ(n) be the maximum. In this paper, we provide the explicit formula for δ(n) and Δ(n).

Work by S.W. Bae was supported by National Research Foundation of Korea(NRF) grant funded by Korea government(MEST)(No. 2011-0005512). Work by Y. Okamoto was supported by Grand-in-Aid for Scientific Research from Ministry of Education, Science and Culture, Japan and Japan Society for the Promotion of Science. Work by C.-S. Shin was supported by research grant funded by Hankuk University of Foreign Studies.

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, Kyonggi University, Korea

    Sang Won Bae

  2. Dept. of Communication Engineering and Informatics, University of Electro-Communications, Japan

    Yoshio Okamoto

  3. Dept. of Digital Information Engineering, Hankuk University of Foreign Studies, Korea

    Chan-Su Shin

Authors
  1. Sang Won Bae
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  2. Yoshio Okamoto
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  3. Chan-Su Shin
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Information Engineering, National Taiwan University, 1 Roosevelt Road, Section 4, 106, Taipei, Taiwan

    Kun-Mao Chao

  2. Institute of Information Science, Academia Sinica, 128 Academia Road, Section 2, 115, Taipei, Taiwan

    Tsan-sheng Hsu

  3. Department of Computer Science and Engineering, National Chung Hsing University, 250 Kuo Kuang Road, 402, Taichung, Taiwan

    Der-Tsai Lee

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© 2012 Springer-Verlag Berlin Heidelberg

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Bae, S.W., Okamoto, Y., Shin, CS. (2012). Area Bounds of Rectilinear Polygons Realized by Angle Sequences. In: Chao, KM., Hsu, Ts., Lee, DT. (eds) Algorithms and Computation. ISAAC 2012. Lecture Notes in Computer Science, vol 7676. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35261-4_65

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  • DOI: https://doi.org/10.1007/978-3-642-35261-4_65

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35260-7

  • Online ISBN: 978-3-642-35261-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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