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Computing the L 1 Geodesic Diameter and Center of a Simple Polygon in Linear Time

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LATIN 2014: Theoretical Informatics (LATIN 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8392))

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Abstract

In this paper, we show that the L 1 geodesic diameter and center of a simple polygon can be computed in linear time. For the purpose, we focus on revealing basic geometric properties of the L 1 geodesic balls, that is, the metric balls with respect to the L 1 geodesic distance. More specifically, in this paper we show that any family of L 1 geodesic balls in any simple polygon has Helly number two, and the L 1 geodesic center consists of midpoints of shortest paths between diametral pairs. These properties are crucial for our linear-time algorithms, and do not hold for the Euclidean case.

S.W. Bae was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2013R1A1A1A05006927). Y. Okamoto was supported by Grant-in-Aid for Scientific Research from Ministry of Education, Science and Culture, Japan, and Japan Society for the Promotion of Science (JSPS). H. Wang was supported in part by NSF under Grant CCF-1317143.

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Author information

Authors and Affiliations

  1. Kyonggi University, Suwon, South Korea

    Sang Won Bae

  2. National Institute of Informatics, Tokyo, Japan

    Matias Korman

  3. Kawarabayashi Large Graph Project, JST, ERATO, Japan

    Matias Korman

  4. The University of Electro-Communications, Tokyo, Japan

    Yoshio Okamoto

  5. Utah State University, Logan, USA

    Haitao Wang

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

Editors and Affiliations

  1. Facultad de Ingeniería, Instituto de Computación, Universidad de la República, Julio Herrera y Reissig 565, 11300, Montevideo, Uruguay

    Alberto Pardo  & Alfredo Viola  & 

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Bae, S.W., Korman, M., Okamoto, Y., Wang, H. (2014). Computing the L 1 Geodesic Diameter and Center of a Simple Polygon in Linear Time. In: Pardo, A., Viola, A. (eds) LATIN 2014: Theoretical Informatics. LATIN 2014. Lecture Notes in Computer Science, vol 8392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54423-1_11

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  • DOI: https://doi.org/10.1007/978-3-642-54423-1_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54422-4

  • Online ISBN: 978-3-642-54423-1

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