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.
CITATION STYLE
Gemsa, A., Lee, D. T., Liu, C. H., & Wagner, D. (2012). Higher order city Voronoi diagrams. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7357 LNCS, pp. 59–70). https://doi.org/10.1007/978-3-642-31155-0_6
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