The Geodesic Diameter of Polygonal Domains

  • Sang Won Bae
  • Matias Korman
  • Yoshio Okamoto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6346)

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(n7.73) or O(n7 (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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Sang Won Bae
    • 1
  • Matias Korman
    • 2
  • Yoshio Okamoto
    • 3
  1. 1.Department of Computer ScienceKyonggi UniversityKorea
  2. 2.Computer Science DepartmentUniversité Libre de Bruxelles (ULB)Belgium
  3. 3.Graduate School of Information Science and EngineeringTokyo Institute of TechnologyTokyoJapan

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