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The Geodesic Diameter of Polygonal Domains

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Algorithms – ESA 2010 (ESA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6346))

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Abstract

This paper studies the geodesic diameter of polygonal domains having h holes and n corners. For simple polygons (i.e., h = 0), it is known that the geodesic diameter is determined by a pair of corners of a given polygon and can be computed in linear time. For general polygonal domains with h ≥ 1, however, no algorithm for computing the geodesic diameter was known prior to this paper. In this paper, we present the first algorithm that computes the geodesic diameter of a given polygonal domain in worst-case time O(n 7.73) or O(n 7 (logn + h)). Among other results, we show the following geometric observation: the geodesic diameter can be determined by two points in its interior. In such a case, there are at least five shortest paths between the points.

Work by S.W. Bae was supported by National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2010-0005974). Work by Y. Okamoto was supported by Global COE Program “Computationism as a Foundation for the Sciences” and Grant-in-Aid for Scientific Research from Ministry of Education, Science and Culture, Japan, and Japan Society for the Promotion of Science.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Kyonggi University, Korea

    Sang Won Bae

  2. Computer Science Department, Université Libre de Bruxelles (ULB), Belgium

    Matias Korman

  3. Graduate School of Information Science and Engineering, Tokyo Institute of Technology, Tokyo, Japan

    Yoshio Okamoto

Authors
  1. Sang Won Bae
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  2. Matias Korman
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  3. Yoshio Okamoto
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computing Science, TU Eindhoven, Eindhoven, The Netherlands

    Mark de Berg

  2. Institute for Computer Science, J.W. Goethe University, 60325, Frankfurt/Main, Germany

    Ulrich Meyer

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Bae, S.W., Korman, M., Okamoto, Y. (2010). The Geodesic Diameter of Polygonal Domains. In: de Berg, M., Meyer, U. (eds) Algorithms – ESA 2010. ESA 2010. Lecture Notes in Computer Science, vol 6346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15775-2_43

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  • DOI: https://doi.org/10.1007/978-3-642-15775-2_43

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15774-5

  • Online ISBN: 978-3-642-15775-2

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