Abstract
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.
Work by S.W. Bae was supported by the Brain Korea 21 Project. Work by M. Korman was supported by MEXT scolarship and CERIES GCOE project, MEXT Japan.
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Bae, S.W., Korman, M., Tokuyama, T. (2009). All Farthest Neighbors in the Presence of Highways and Obstacles . In: Das, S., Uehara, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2009. Lecture Notes in Computer Science, vol 5431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00202-1_7
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DOI: https://doi.org/10.1007/978-3-642-00202-1_7
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