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Farthest Voronoi Diagrams under Travel Time Metrics

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7157))

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Abstract

Given a set of roads in the plane with assigned speed, a traveler is assumed to move at the specified speed along each road, and at unit speed out of the roads. We are interested in the minimum travel time when we travel from one point in the plane to another, which defines a travel time metric. We study the farthest Voronoi diagram under this travel time metric, providing first nontrivial bounds on its combinatorial and computational complexity. Our approach is based on structural observations and recently known algorithmic technique. In particular, we show that if we are given a set of m isothetic roads with equal speed, then the diagram of n sites on the L 1 plane has Θ(nm) complexity and can be computed in O(nmlog3(n + m)) time in the worst case.

Work by S.W.Bae was supported by National Research Foundation of Korea(NRF) grant funded by the Korea government(MEST) (No. 2011-0005512).

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Author information

Authors and Affiliations

  1. Department of Computer Science, Kyonggi University, Suwon, Korea

    Sang Won Bae

  2. Department of Computer Science, Korea Advanced Institute of Science and Technology, Daejeon, Korea

    Kyung-Yong Chwa

Authors
  1. Sang Won Bae
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  2. Kyung-Yong Chwa
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Editor information

Editors and Affiliations

  1. Graph Drawing and Information Visualization Laboratory, Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology, Bangladesh

    Md. Saidur Rahman

  2. , Faculty of Engineering, Department of Computer Science, Gunma University, 1-5-1 Tenjin-Cho, 376-8515, Kiryu-Shi, Japan

    Shin-ichi Nakano

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Bae, S.W., Chwa, KY. (2012). Farthest Voronoi Diagrams under Travel Time Metrics. In: Rahman, M.S., Nakano, Si. (eds) WALCOM: Algorithms and Computation. WALCOM 2012. Lecture Notes in Computer Science, vol 7157. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28076-4_6

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  • DOI: https://doi.org/10.1007/978-3-642-28076-4_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28075-7

  • Online ISBN: 978-3-642-28076-4

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