Higher Order City Voronoi Diagrams

  • Andreas Gemsa
  • D. T. Lee
  • Chih-Hung Liu
  • Dorothea Wagner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7357)

Abstract

We investigate higher-order Voronoi diagrams in the city metric. This metric is induced by quickest paths in the L 1 metric in the presence of an accelerating transportation network of axis-parallel line segments. For the structural complexity of k th-order city Voronoi diagrams of n point sites, we show an upper bound of O(k(n − k) + kc) and a lower bound of Ω(n + kc), where c is the complexity of the transportation network. This is quite different from the bound O(k(n − k)) in the Euclidean metric [12]. For the special case where k = n − 1 the complexity in the Euclidean metric is O(n), while that in the city metric is Θ(nc). Furthermore, we develop an O(k 2(n + c)log(n + c))-time iterative algorithm to compute the k th-order city Voronoi diagram and an O(nclog2(n + c)logn)-time divide-and-conquer algorithm to compute the farthest-site city Voronoi diagram.

Keywords

Voronoi Diagram Transportation Network Point Site Voronoi Region Voronoi Edge 
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

  • Andreas Gemsa
    • 1
  • D. T. Lee
    • 2
    • 3
  • Chih-Hung Liu
    • 1
    • 2
  • Dorothea Wagner
    • 1
  1. 1.Karlsruhe Institute of TechnologyGermany
  2. 2.Academia SinicaTaiwan
  3. 3.National Chung Hsing UniversityTaiwan

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