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Abstract: We show that the wavefront approach to Voronoi diagrams (a deterministic line-sweep algorithm that does not use geometric transform) can be generalized to distance measures more general than the Euclidean metric. In fact, we provide the first worst-case optimal (O(n log n) time, O(n) space) algorithm that is valid for the full class of what has been called nice metrics in the plane. This also solves the previously open problem of providing an O(n log n)-time plane-sweep algorithm for arbitrary... (Update)
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...to rectilinear layouts. The time complexity is O(n log n) and it is based on the wavefront paradigm introduced by Dehne and Klein [3] for the Voronoi diagram of points. s s L spike event wavefront Figure 10: Construction of the Voronoi diagram by plane sweep method. We...
...a nite number of connected components. Hence, property (v) holds too. 2 As a consequence of this theorem, the sweep line algorithm in [4] can be used for computing the Voronoi Diagram, and we get the following result. Corollary 6 The Voronoi Diagram of a set of n points with...
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0.2: Improving Worst-Case Optimal Delaunay Triangulation Algorithms - Leach (1992) (Correct)
0.2: Convex Distance Functions in 3-Space are Different - Icking, Klein, Lê, Ma (1994) (Correct)
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BibTeX entry: (Update)
F. Dehne and R. Klein, "The Big Sweep: On the power of the Wavefront Approach to Voronoi Diagrams," Algorithmica(1997), 17, 19-32. http://citeseer.ist.psu.edu/article/dehne97big.html More
@inproceedings{ dehne94big,
author = "Dehne and Klein",
title = "``The Big Sweep'': On the Power of the Wavefront Approach to Voronoi Diagrams",
booktitle = "{MFCS}: Symposium on Mathematical Foundations of Computer Science",
year = "1994",
url = "citeseer.ist.psu.edu/article/dehne97big.html" }
Citations (may not include all citations):335 Applications of random sampling in computational geometry - Clarkson, Shor - 1989
159 A sweepline algorithm for Voronoi diagrams (context) - Fortune - 1987
94 Closest-point problems (context) - Shamos, Hoey - 1975
51 Voronoi diagrams based on convex distance functions (context) - Chew - 1985
47 Voronoi diagrams from convex hulls (context) - Brown - 1979
39 the construction of abstract Voronoi diagrams (context) - Mehlhorn, Meiser et al. - 1991
39 the construction of abstract Voronoi diagrams (context) - Klein, Mehlhorn et al. - 1990
37 Concrete and Abstract Voronoi diagrams (context) - Klein - 1989
21 Voronoi diagrams and arrangements (context) - Edelsbrunner, Seidel - 1986
20 Dynamic computational geometry (context) - Atallah - 1985
17 Constrained Delaunay Triangulations and Voronoi Diagrams wit.. (context) - Seidel - 1988
17 Voronoi diagrams---a survey of a fundamental data structure (context) - Aurenhammer - 1991
16 Voronoi diagrams based on general metrics in the plane (context) - Klein, Wood - 1988
10 Voronoi diagrams based on strictly convex distances on the p.. (context) - Mazon, Recio - 1991
9 Abstract Voronoi diagrams and their applications (context) - Klein - 1988
8 Reported by C (context) - Cole - 1989
8 Convex distance functions in 3D are different (context) - Icking, Klein et al. - 1993
5 A sweepcircle algorithm for Voronoi diagrams (context) - Dehne, Klein - 1988
3 plane-sweep algorithm for L 1 and L (context) - Shute, Deneen et al.
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