Higher order city voronoi diagrams

Authors:
Andreas Gemsa;D. T. Lee;Chih-Hung Liu;Dorothea Wagner
Affiliations:
Karlsruhe Institute of Technology, Germany;Academia Sinica, Taiwan,National Chung Hsing University, Taiwan;Karlsruhe Institute of Technology, Germany,Academia Sinica, Taiwan;Karlsruhe Institute of Technology, Germany
Venue:
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Year:
2012

Citing 8
Cited 1

Optimal point location in a monotone subdivision

SIAM Journal on Computing
An improved algorithm for constructing kth-order voronoi diagrams

IEEE Transactions on Computers
A fast planar partition algorithm, I

Journal of Symbolic Computation
On levels in arrangements and Voronoi diagrams

Discrete & Computational Geometry
Constructing Levels in Arrangements and Higher Order Voronoi Diagrams

SIAM Journal on Computing
On k-Nearest Neighbor Voronoi Diagrams in the Plane

IEEE Transactions on Computers
Farthest-polygon Voronoi diagrams

Computational Geometry: Theory and Applications
Shortest paths and voronoi diagrams with transportation networks under general distances

ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation

Optimal time-convex hull under the Lp metrics

WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures

Quantified Score

Hi-index	0.00

Visualization

Abstract

We investigate higher-order Voronoi diagrams in the city metric. This metric is induced by quickest paths in the L1 metric in the presence of an accelerating transportation network of axis-parallel line segments. For the structural complexity of kth-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(k2(n+c)log(n+c))-time iterative algorithm to compute the kth-order city Voronoi diagram and an O(nclog2(n+c)logn)-time divide-and-conquer algorithm to compute the farthest-site city Voronoi diagram.