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Applications of Random Sampling to On-line Algorithms in Computational Geometry (1992)  (Make Corrections)  (53 citations)
Jean-Daniel Boissonnat, Olivier Devillers, René Schott, Monique Teillaud, Mariette Yvinec
Discrete and Computational Geometry



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Abstract: This paper presents a general framework for the design and randomized analysis of geometric algorithms. These algorithms are on-line and the framework provides general bounds for their expected space and time complexities when averaging over all permutations of the input data. The method is general and can be applied to various geometric problems. The power of the technique is illustrated by new efficient on-line algorithms for constructing convex hulls and Voronoi diagrams in any... (Update)

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Voronoi Diagrams - Aurenhammer, Klein   (Correct)
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39:   Applications of random sampling in computational geometry - Clarkson, Shor - 1989
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BibTeX entry:   (Update)

J.-D. Boissonnat, O. Devillers, R. Schott, M. Teillaud, and M. Yvinec. Applications of random sampling to on-line algorithms in computational geometry. Discrete Comput. Geom., 8:51--71, 1992. http://citeseer.ist.psu.edu/boissonnat92applications.html   More

@article{ boissonnat92applications,
    author = "Jean-Daniel Boissonnat and Olivier Devillers and Ren{\'e} Schott and Monique Teillaud and Mariette Yvinec",
    title = "Applications of Random Sampling to On-Line Algorithms in Computational Geometry",
    journal = "Discrete and Computational Geometry",
    volume = "8",
    pages = "51--71",
    year = "1992",
    url = "citeseer.ist.psu.edu/boissonnat92applications.html" }
Citations (may not include all citations):
481   Algorithms on Combinatorial Geometry (context) - Edelsbrunner - 1987
335   Applications of random sampling in computational geometry - Clarkson, Shor - 1989
114   An optimal algorithm for intersecting line segments in the p.. (context) - Chazelle, Edelsbrunner - 1988
108   Combinatorial complexity bounds for arrangements of curves a.. (context) - Clarkson, Edelsbrunner et al. - 1990
101   Randomized incremental construction of Delaunay and Voronoi .. (context) - Guibas, Knuth et al. - 1992
56   Constructing higher-dimensional convex hulls at logarithmic .. (context) - Seidel - 1986
41   the randomized construction of the Delaunay tree - Boissonnat, Teillaud
39   the construction of abstract Voronoi diagrams (context) - Mehlhorn, Meiser et al. - 1991
38   Higher-dimensional Voronoi diagrams in linear expected time (context) - Dwyer - 1991
34   Constructing the visibility graph for n line segments in O (context) - Welzl - 1985
24   A hierarchical representation of objects: The Delaunay Tree (context) - Boissonnat, Teillaud - 1986
11   A semi-dynamic construction of higher order Voronoi diagrams.. - Boissonnat, Devillers et al. - 1990
6   On obstruction in relation to a fixed viewpoint (context) - Mulmuley - 1989
5   Simple on-line algorithms for convex polygons (context) - Avis, ElGindy et al. - 1985
4   A convex hull algorithm optimal for point sites in even dime.. (context) - Seidel - 1981



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