K. Mehlhorn, S. Meiser, and R. Rasch, Furthest site abstract Voronoi diagrams, Technical Report MPI-I-92-135, Max-Planck-Institut fur Informatik, Saarbrucken, Germany. 11  Home/Search Document Details and Download
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Voronoi Diagrams for Convex Polygon-Offset Distance.. - Barequet, Dickerson.. (2000) (Correct)
....a set S of n points in the plane, with distance defined by a scaling of an m edge convex polygon. This is actually quite close to optimal for fully constructing the Voronoi diagram, as they show that such a diagram can be of size #(nm) Klein, Mehlhorn, Meiser, and others [Kl] KMM] KW] MMO] [MMR] generalized this work even further, showing how to define Voronoi diagrams in a very abstract setting. They also give 1 Intuitively speaking, offsetting a polygon is done by locally shifting all its edge. We give a precise definition later in the paper. Voronoi Diagrams for Convex ....
....the contra positive of Minkowski s characterization theorem, but we provide a simple constructive proof. In spite of this fact, however, we show that convex polygon offset distance functions nevertheless satisfy all the topological properties for abstract Voronoi diagrams [Kl] KMM] KW] MMO] [MMR]. Finally, given a set S of n points in the plane, we show how to construct compact representations of nearestand furthest site Voronoi diagrams deterministically for S with respect to an offset distance defined by an m edge convex polygon in O(n(log n log 2 m) m) time. We use the ....
[Article contains additional citation context not shown here]
K. Mehlhorn, S. Meiser, and R. Rasch, Furthest Site Abstract Voronoi Diagrams, Technical Report MPI-I-92-135, Max-Planck-Institut fur Informatik, Saarbrucken, 1992.
Voronoi Diagrams for Polygon-Offset Distance Functions - Barequet, Dickerson, Goodrich (1997) (Correct)
....log n) time method for constructing such diagrams for a set S of n points in the plane, with distance defined by a scaling of an m edge convex polygon. This is actually quite close to optimal, as they show the Voronoi diagram can be of size Theta(nm) This work was generalized even further [Kl, KMM, KW, MMO, MMR], showing how to define Voronoi diagrams in a very abstract setting. They also give randomized incremental constructions for this abstract setting that can be applied to nearest and furthest neighbor Voronoi diagrams for convex distance functions. The running times of these constructions are ....
....the triangle inequality. This, of course, follows from the contra positive of Minkowski s characterization theorem, but we provide a simple constructive proof. Nevertheless, we show that convex polygon offset distance functions satisfy all the topological properties for abstract Voronoi diagrams [Kl, KMM, KW, MMO, MMR]. Finally, given a set S of n points in the plane, we show how to deterministicly construct compact representations of nearest and furthest site Voronoi diagrams for S with respect to an offset distance defined by an m edge convex polygon in O(n(log n log m) m) time. We apply the tentative ....
[Article contains additional citation context not shown here]
K. Mehlhorn, S. Meiser, and R. Rasch, Furthest site abstract Voronoi diagrams, Technical Report MPI-I-92-135, Max-Planck-Institut fur Informatik, Saarbrucken, Germany.
Annulus Placement Problems for Scaled and Offset.. - Barequet, Bose.. (Correct)
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K. Mehlhorn, S. Meiser, and R. Rasch, Furthest site abstract Voronoi diagrams, Technical Report MPI-I-92-135, Max-Planck-Institut fur Informatik, Saarbrucken, Germany. 11
Vertical Decomposition of Shallow Levels in 3-Dimensional .. - Agarwal, Efrat, Sharir (1995) (15 citations) (Correct)
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K. Mehlhorn, S. Meiser, and R. Rasch, Furthest site abstract Voronoi diagrams, Tech. Report, Max-Planck Institut fur Informatik, Saarbrucken, 1992.
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