Higher order city Voronoi diagrams
Journal
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Journal Volume
7357 LNCS
Pages
59-70
Date Issued
2012
Author(s)
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(nclog 2(n + c)logn)-time divide-and-conquer algorithm to compute the farthest-site city Voronoi diagram. © 2012 Springer-Verlag.
Other Subjects
Divide-and-conquer algorithm; Euclidean metrics; Higher order; Higher-order Voronoi diagrams; Iterative algorithm; Line segment; Lower bounds; Structural complexity; Transportation network; Upper Bound; Voronoi diagrams; Algorithms; Computational geometry; Graphic methods
Type
conference paper