In the Hausdorff Voronoi diagram of a family of clusters of points in the plane, the distance between a point t and a cluster P is measured as the maximum distance between t and any point in P, and the diagram is defined in a nearest-neighbor sense for the input clusters. In this paper we consider non-crossing clusters in the plane, for which the combinatorial complexity of the Hausdorff Voronoi diagram is linear in the total number of points, n, on the convex hulls of all clusters. We present a randomized incremental construction, based on point location, that computes this diagram in expected O(n log 2 n) time and expected O(n) space. Our techniques efficiently handle non-standard characteristics of generalized Voronoi diagrams, such as sites of non-constant complexity, sites that are not enclosed in their Voronoi regions, and empty Voronoi regions. The diagram finds direct applications in VLSI computeraided design.
Abstract. Stabbing a set S of n segments in the plane by a line is a well-known 8 problem. In this paper we consider the variation where the stabbing object is a cir-9 cle instead of a line. We show that the problem is tightly connected to two cluster
10Voronoi diagrams, in particular, the Hausdorff and the farthest-color Voronoi dia-11 gram. Based on these diagrams, we provide a method to compute a representation 12 of all the combinatorially different stabbing circles for S, and the stabbing circles 13 with maximum and minimum radius. We give conditions under which our method 14 is fast. These conditions are satisfied if the segments in S are parallel, resulting in 15 a O(n log 2 n) time and O(n) space algorithm. We also observe that the stabbing
Abstract. Stabbing a set S of n segments in the plane by a line is a well-known 8 problem. In this paper we consider the variation where the stabbing object is a cir-9 cle instead of a line. We show that the problem is tightly connected to two cluster
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