All Farthest Neighbors in the Presence of Highways and Obstacles

  • Sang Won Bae
  • Matias Korman
  • Takeshi Tokuyama
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5431)


We consider the problem of computing all farthest neighbors (and the diameter) of a given set of n points in the presence of highways and obstacles in the plane. When traveling on the plane, travelers may use highways for faster movement and must avoid all obstacles. We present an efficient solution to this problem based on knowledge from earlier research on shortest path computation. Our algorithms run in \(\ensuremath{O(nm(\log m + \log^2n))}\) time using O(m + n) space, where the m is the combinatorial complexity of the environment consisting of highways and obstacles.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Sang Won Bae
    • 1
  • Matias Korman
    • 2
  • Takeshi Tokuyama
    • 2
  1. 1.Division of Computer ScienceKAISTKorea
  2. 2.Graduate School of Information SciencesTohoku UniversitySendaiJapan

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