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)


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.


Short Path Line Segment Geodesic Distance Simple Polygon Geodesic Ball 
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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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