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  Efficient randomized algorithms for some geometric optimization problems (1996) [39 citations — 14 self]

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by Pankaj K. Agarwal, Micha Sharir
Discrete Comput. Geom
http://www.math.tau.ac.il/~sharir/asrand.ps
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Abstract:

In this paper we first prove the following combinatorial bound, concerning the complexity of the vertical decomposition of the minimization diagram of trivariate functions: Let F be a collection of n totally- or partially-defined algebraic trivariate functions of constant maximum degree, with the additional property that, for a given pair of functions f; f 0

Citations

351 Applications of random sampling in computational geometry – Clarkson, Shor - 1989
331 Davenport-Schinzel Sequences and Their Geometric Applications – Sharir, Agarwal - 1995
243 Applying parallel computation algorithms in the design of serial algorithms – Megiddo - 1983
192 Epsilon nets and simplex range queries – Haussler, Welzl - 1987
172 Linear Programming in Linear Time When the Dimension Is Fixed – Megiddo - 1984
135 Combinatorial complexity bounds for arrangements of curves and spheres, Discrete and Comput – Clarkson, Edelsbrunner, et al. - 1990
73 Almost tight upper bounds for lower envelopes in higher dimensions, Discrete Comput – Sharir - 1994
61 Computing the width of a set – Houle, Toussaint - 1988
50 An expander-based approach to geometric optimization – Katz, Sharir - 1997
39 width, closest line pair, and parametric searching, Discrete Comput – Chazelle, Edelsbrunner, et al. - 1993
38 The polygon containment problem – Chazelle - 1983
38 Roundness algorithms using the Voronoi diagrams – Ebara, Fukuyama, et al. - 1989
32 Randomized optimal algorithm for slope selection – MATOUSEK - 1995
30 A randomized algorithm for slope selection – Dillencourt, Mount, et al. - 1992
30 Out-of-roundness problem revisited – Lee - 1991
27 On lazy randomized incremental construction – Berg, Dobrindt, et al.
26 Optimal slope selection via expanders – Katz, Sharir - 1993
24 Optimal slope selection via cuttings – Brönnimann, Chazelle - 1998
24 A singly exponential stratification scheme for real semi-algebraic varieties and its application – Chazelle, Edelsbrunner, et al. - 1989
24 An Optimal Algorithm for Roundness Determination on Convex Polygons – Swanson, Lee, et al. - 1995
19 On lazy randomized incremental construction – Berg, Dobrindt, et al. - 1994
17 An algorithm for generalized point location and its applications – Chazelle, Sharir - 1990
14 Vertical decompositions for triangles – Berg, Guibas, et al. - 1994
14 A Book of Curves – Lockwood - 1961
11 The overlay of lower envelopes in three dimensions and its applications – Agarwal, Schwarzkopf, et al. - 1995
10 Computing lower envelopes in four dimensions with applications – Agarwal, Aronov, et al. - 1994
10 New applications of parametric searching in computational geometry – Agarwal, Sharir, et al. - 1994
8 On collision-free placements of simplices and the closest pair of lines in 3-space – Pellegrini - 1994
6 The biggest diagonal in a simple polygon – Aggarwal, Suri - 1990
6 On the width and roundness of a set of points – Smid, Janardan - 1995
3 New bounds for lower envelopes in 3 dimensions, with applications to visibility in terrains, Discrete Comput – Halperin, Sharir - 1994
2 private communication. Geometric Optimization – Wilfong - 1995