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Abstract: We give fast randomized and deterministic parallel methods for constructing convex hulls in IR d , for any fixed d. Our methods are for the weakest shared-memory model, the EREW PRAM, and have optimal work bounds (with high probability for the randomized methods). In particular, we show that the convex hull of n points in IR d can be constructed in O(logn) time using O(n log n + n bd=2c ) work, with high probability. We also show that it can be constructed deterministically in O(log 2 ... (Update)
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...work and O(log 3 n) paallel time. We can alternatively use the random ized parallel algorithms of Reif and Sen [28] or by Amaro et al. [1], in both two and three dimensions. Both of these randomized parallel Delaunay triangulation algorithms have expected parallel running...
...can be developed for computing the intersection of n congruent balls in 3 space. This has been answered in the affirmative by Amato et al. [34], following a series of near linear time but weaker deterministic algorithms [60, 206, 237] Amato et al. derandomized the Clarkson...
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0.9: A Time-Optimal Parallel Algorithm for 3D Convex Hulls - Amato, Preparata (1993) (Correct)
0.7: Computing Faces in Segment and Simplex Arrangements - Amato, Goodrich, Ramos (1995) (Correct)
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BibTeX entry: (Update)
N.M. Amato, M.T. Goodrich, and E.A. Ramos. Parallel algorithms for higher-dimensionalconvex hulls. In Proc. 35th Annu. IEEE Sympos. Found. Comput. Sci. (FOCS 93), pages 683--694, 1994. http://citeseer.ist.psu.edu/amato94parallel.html More
@inproceedings{ amato94parallel,
author = "Nancy M. Amato and Michael T. Goodrich and Edgar A. Ramos",
title = "Parallel Algorithms for Higher-Dimensional Convex Hulls",
booktitle = "{IEEE} Symposium on Foundations of Computer Science",
pages = "683-694",
year = "1994",
url = "citeseer.ist.psu.edu/amato94parallel.html" }
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335 Applications of random sampling in computational geometry - Clarkson, Shor - 1989
227 Parallel merge sort (context) - Cole - 1988
199 A simple parallel algorithm for the maximal independent set .. (context) - Luby - 1986
185 Applying parallel computation algorithms in the design of se.. (context) - Megiddo - 1983
165 Three-dimensional alpha shapes - Edelsbrunner, Mucke - 1994
115 the density of families of sets (context) - Sauer - 1972
99 Information Processing Letters (context) - Hagerup, Rub et al. - 1990
98 volume 10 of EATCS Monographs on Theoretical Computer Scienc.. (context) - Edelsbrunner, Combinatorial - 1987
94 Upper and lower time bounds for parallel random access machi.. (context) - Cook, Dwork et al. - 1986
91 Epsilon-nets and simplex range queries (context) - Haussler, Welzl - 1987
87 Applications of parametric searching in geometric optimizati.. - Agarwal, Sharir et al. - 1992
80 Slowing down sorting networks to obtain faster sorting algor.. (context) - Cole - 1987
79 Cutting hyperplanes for divide-and-conquer (context) - Chazelle - 1993
75 A deterministic view of random sampling and its use in geome.. (context) - Chazelle, Friedman - 1990
73 Fast detection of polyhedral intersection (context) - Dobkin, Kirkpatrick - 1983
72 Efficient partition trees (context) - Matousek - 1992
69 Small-dimensional linear programming and convex hulls made e.. (context) - Seidel - 1991
68 An efficient algorithm for determining the convex hull of a .. (context) - Graham - 1972
64 The ultimate planar convex hull algorithm (context) - Kirkpatrick, Seidel - 1986
62 Parallel computational geometry (context) - Aggarwal, Chazelle et al. - 1988
58 Reporting points in halfspaces (context) - Matousek - 1992
56 Constructing higher-dimensional convex hulls at logarithmic .. (context) - Seidel - 1986
53 Convex hulls of finite sets of points in two and three dimen.. (context) - Preparata, Hong - 1977
47 part i: the basic technique with applications to optimal par.. (context) - Cole, Vishkin et al. - 1988
47 Converting high probability into nearlyconstant time---with .. - Matias, Vishkin - 1991
45 Multidimensional searching problems (context) - Dobkin, Lipton - 1976
43 An optimal convex hull algorithm in anyfixed dimension (context) - Chazelle - 1993
43 Approximations and optimal geometric divide-andconquer (context) - Matousek - 1991
41 Removing randomness in parallel computation without a proces.. - Luby - 1988
31 Parallel dictionaries on 2-3 trees (context) - Paul, Vishkin et al. - 1983
31 Cutting hyperplane arrangements (context) - Matousek - 1991
28 Geometric partitioning made easier (context) - Goodrich - 1993
26 closest line pair and parametric searching (context) - Chazelle, Edelsbrunner et al. - 1993
24 Derandomizing an output-sensitive convex hull algorithm in t.. (context) - Chazelle, Matousek - 1992
23 Product range spaces (context) - Bronnimann, Chazelle et al. - 1993
23 Efficient parallel convex hull algorithms (context) - Miller, Stout - 1988
22 A deterministic algorithm for the three-dimensional diameter.. - Matousek, Schwarzkopf - 1993
20 Randomized algorithms for binary search and load balancing o.. - Reif, Sen - 1990
19 Parallel algorithms for some functions of two convex polygon.. (context) - Atallah, Goodrich - 1988
18 Optimal parallel randomized algorithms for three-dimensional.. (context) - Reif, Sen - 1992
15 Efficient parallel solutions to some geometric problems (context) - Atallah, Goodrich - 1986
15 Parallel algorithms for geometricproblems (context) - Chow - 1980
13 wise independent randomvariables (context) - Karloff, Mansour et al. - 1994
13 A convex hull algorithm optimal for point sets in even dimen.. (context) - Seidel - 1981
11 Beweis einer vermutung von (context) - Heppes - 1956
10 Densite et dimension (context) - Assouad - 1983
8 Optimal parallel randomized algorithms for the Voronoi diagr.. (context) - Rajasekaran, Ramaswami - 1994
7 On point location and motion planning among simplicies - Pellegrini - 1994
7 convexhull problem revisited (context) - Amato, Preparata - 1992
4 Constructing arrangements optimally in parallel (context) - Goodrich - 1993
3 the uniform convergenceof relative frequencies of events to .. (context) - Vapnik, Chervonenkis - 1971
3 convex hull algorithm (context) - Amato, Preparata et al. - 1993
2 An algorithm for intersecting equal radius balls r (context) - Ramos - 1994
1 Parallel constructionof subdivision hierarchies (context) - Dadounand, Kirkpatrick - 1989
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