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Computing the L1 Geodesic Diameter and Center of a Simple Polygon in Linear Time

  • Sang Won Bae
  • Matias Korman
  • Yoshio Okamoto
  • Haitao Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8392)

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.

Keywords

Short Path Line Segment Geodesic Distance Simple Polygon Geodesic Ball 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Sang Won Bae
    • 1
  • Matias Korman
    • 2
    • 3
  • Yoshio Okamoto
    • 4
  • Haitao Wang
    • 5
  1. 1.Kyonggi UniversitySuwonSouth Korea
  2. 2.National Institute of InformaticsTokyoJapan
  3. 3.Kawarabayashi Large Graph ProjectJST, ERATOJapan
  4. 4.The University of Electro-CommunicationsTokyoJapan
  5. 5.Utah State UniversityLoganUSA

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