Farthest Voronoi Diagrams under Travel Time Metrics

(Extended Abstract)
  • Sang Won Bae
  • Kyung-Yong Chwa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7157)


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.


Short Path Voronoi Diagram Transportation Network Medial Edge Minimum Travel Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sang Won Bae
    • 1
  • Kyung-Yong Chwa
    • 2
  1. 1.Department of Computer ScienceKyonggi UniversitySuwonKorea
  2. 2.Department of Computer ScienceKorea Advanced Institute of Science and TechnologyDaejeonKorea

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