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Parallel randomized techniques for some fundamental geometric problems: A survey [chapter]

Suneeta Ramaswami
1998 Lecture Notes in Computer Science  
In 20 , Reif and Sen gave an optimal parallel randomized algorithm on the CREW PRAM for the construction of the convex hull of points in three dimensions.  ...  The important problems of constructing convex hulls of points in three dimensions and Voronoi diagrams of points in two dimensions , h o wever, eluded optimal parallel solutions for a long time.  ...  It is hoped, however, that the selected results demonstrate the e ectiveness of randomization in parallel algorithm design for problems in computational geometry.  ... 
doi:10.1007/3-540-64359-1_714 fatcat:qaoirqoybrdtxh322pvryxjgxq

Page 3890 of Mathematical Reviews Vol. , Issue 98F [page]

1998 Mathematical Reviews  
A. (1-PURD-E; West Lafayette, IN) A randomized parallel three-dimensional convex hull algorithm for coarse-grained multicomputers.  ...  Summary: “We present a randomized parallel algorithm for constructing the three-dimensional convex hull on a generic p-processor coarse-grained multicomputer with arbitrary inter- connection network and  ... 

Page 3640 of Mathematical Reviews Vol. , Issue 85h [page]

1985 Mathematical Reviews  
G. (3-QEN-C) 85h:68076 Optimal parallel algorithms for computing convex hulls and for sorting. (German summary) Computing 33 (1984), no. 1, 1-11.  ...  Author’s summary: “A parallel algorithm is presented for comput- ing the convex hull of a set of n points in the plane.  ... 

GPU accelerated convex hull computation

Min Tang, Jie-yi Zhao, Ruo-feng Tong, Dinesh Manocha
2012 Computers & graphics  
We present a hybrid algorithm to compute the convex hull of points in three or higher dimensional spaces.  ...  by 10 − 27 times (for static point sets) and 22 − 46 times (for deforming point sets).  ...  [4, 8] proposed randomized and deterministic parallel methods for constructing a convex hull in parallel and proved that the convex hull in d-dimensional space can be constructed in O(nlogn + n d/2  ... 
doi:10.1016/j.cag.2012.03.015 fatcat:vjsmjtv4u5fi3kyvp7ayckvl4e

A Randomized Parallel Three-Dimensional Convex Hull Algorithm for Coarse-Grained Multicomputers

F. Dehne, X. Deng, P. Dymond, A. Fabri, A. A. Khokhar
1997 Theory of Computing Systems  
For any given set of n points in 3-space, the algorithm computes the three-dimensional convex hull, with high probability, in O((n log n)/ p) local computation time and O(1) communication phases with at  ...  We present a randomized parallel algorithm for constructing the threedimensional convex hull on a generic p-processor coarse-grained multicomputer with arbitrary interconnection network and n/ p local  ...  The Three-Dimensional Convex Hull Problem For the three-dimensional convex hull problem studied in this paper, Amato and Preparata [5] give an almost work optimal deterministic NC 1 algorithm for the  ... 
doi:10.1007/s002240000067 fatcat:outcwc7vqfdzlmlod7wriubpza

Parallel algorithms in geometry [chapter]

Michael Goodrich
2004 Handbook of Discrete and Computational Geometry, Second Edition  
Is there an efficient output-sensitive parallel convex hull algorithm for d ≥ 4?3. Is there an optimal-work O(log 2 n)-time CREW PRAM convex hull algorithm for odd dimensions greater than 4?  ...  few of these algorithms to illustrate their flavor. 2-DIMENSIONAL CONVEX HULLS The two-dimensional convex hull algorithm of Miller and Stout [MS88] is based upon a parallel divide-and-conquer scheme  ... 
doi:10.1201/9781420035315.ch42 fatcat:bjv5rzaoxne5tjle6ppvondlam

Maximum overlap and minimum convex hull of two convex polyhedra under translations

Hee-Kap Ahn, Peter Brass, Chan-Su Shin
2008 Computational geometry  
Given two convex polyhedra P and Q in three-dimensional space, we consider two related problems of shape matching: (1) finding a translation t 1 ∈ R 3 of Q that maximizes the volume of their overlap P  ...  For the maximum overlap problem, we observe that the dth root of the objective function is concave and present an algorithm that computes the optimal translation in expected time O(n 3 log 4 n).  ...  The two-dimensional version of this problem for two convex polygons has been studied by Ahn and Cheong [1] : with a fixed orientation they proposed an exact near-linear time algorithm for finding an optimal  ... 
doi:10.1016/j.comgeo.2007.08.001 fatcat:n5uoshjeqfaixn7sd3wzu5opnm

Page 4361 of Mathematical Reviews Vol. , Issue 96g [page]

1996 Mathematical Reviews  
P. (1-BRN-C; Providence, RI) A time-optimal parallel algorithm for three-dimensional convex hulls. (English summary) Algorithmica 14 (1995), no.2, 169-182.  ...  The contributions of this paper are therefore (i) an O(logn)-time parallel algorithm for the three-dimensional convex hull problem, and (ii) a paral- lel algorithm for this problem that does not follow  ... 

Faster output-sensitive parallel algorithms for 3D convex hulls and vector maxima

Neelima Gupta, Sandeep Sen
2003 Journal of Parallel and Distributed Computing  
In this paper we focus on the problem of designing very fast parallel algorithms for the convex hull and the vector maxima problems in three dimensions that are output-size sensitive.  ...  We also present an optimal speed-up (with respect to the input size only) sublogarithmic time algorithm that uses superlinear number of processors for vector maxima in three dimensions. r  ...  In the context of parallel algorithms, for convex hulls in three dimensions (3-D hulls) Chow [Cho80] described an Oðlog 3 nÞ time algorithm using n CREW processors.  ... 
doi:10.1016/s0743-7315(03)00035-2 fatcat:l27fsx5wb5alzhl2bv3lmgatdm

Data Mining Analysis and High-dimensional Visualization Based on Electric Big Data

Qian Sun, Bo Zhu, Qiang Li, Tingjun Yang
2017 DEStech Transactions on Engineering and Technology Research  
through parallel coordinate system based on convex hull optimization.  ...  By collecting data based on optimized scatter diagram in non-linear polynomial form, power supply companies can accurately analyze and display users' power utility habits in more dimensions and angles  ...  The description for parallel coordinate optimization algorithm based on convex algorithm is as follows: Input: high-dimensional datasets, category number of dataset is C; Output: optimized high-dimensional  ... 
doi:10.12783/dtetr/iceta2016/7057 fatcat:njivsiljerbzjhoqgmn57vdtl4

Polling: a new randomized sampling technique for computational geometry

J. H. Reif, S. Sen
1989 Proceedings of the twenty-first annual ACM symposium on Theory of computing - STOC '89  
The best known deterministic parallel algorithms for 2-D Voronoi-diagram and 3-D Convex hull run in O(log2 n) and O(log2 nlog * n) time respectively while using O(n) processors.  ...  Because of well-known reductions, our methods also yield equally efficient algorithms for fundamental problems like t,he convex hull in three dimensions, Voronoi diagram of point sites on a plane and Euclidean  ...  In this paper we actually describe an optimal randomized parallel algorithm for constructing convex hulls in Euclidean 3-space.  ... 
doi:10.1145/73007.73045 dblp:conf/stoc/ReifS89 fatcat:mtfext2ncrbtjlqu2hz4qokqsu

A randomized parallel 3D convex hull algorithm for coarse grained multicomputers

Frank Dehne, Xiaotie Deng, Patrick Dymond, Andreas Fabri, Ashfaq A. Khokhar
1995 Proceedings of the seventh annual ACM symposium on Parallel algorithms and architectures - SPAA '95  
We present a randomized parallel algorithm for constructing the 3D convex hull on a generic p-processor coarse grained multicomputer with arbitrary inter-  ...  Hence, we obtain Requirement 1 f2(ln(n)) < k <5 In order to compute the convex hull CH(R) of R we apply any optimal sequential (0(~log2~) time) 3D convex hull algorithm [35, 15].  ...  Finally, we note that our algorithm can also be transformed into an optimal O(log n) time PRAM algorithm.  ... 
doi:10.1145/215399.215410 dblp:conf/spaa/DehneDDFK95 fatcat:is3euybf4nferah244bf4dq3ba

Convex hulls of finite sets of points in two and three dimensions

F. P. Preparata, S. J. Hong
1977 Communications of the ACM  
Since the convex hull of a simple n-gon may be computed in O(n) time [6], [7], step 1 may be changed to give an O(n) time algorithm for simple n-gons.  ...  Three-Dimensional Width Algorithm We now extend the method used in Section 2-C to solve the three-dimensional width problem.  ...  A modification of Brown's algorithm for finding the diameter of a convex polyhedron in three dimensions computes the width in O(n + I) time, where I is the number of pairs of edges  ... 
doi:10.1145/359423.359430 fatcat:rke3cem5grfpjkw5spk5rmp7i4

An efficient planar incremental convex hull algorithm to find the edges of the boundary polygon of the convex hull of a set of points

K. R. Wijeweera, S. R. Kodituwakku
2021 Ceylon Journal of Science  
The optimal time complexity for insertion of a point in existing incremental convex hull algorithms is O (n).  ...  RESEARCH ARTICLE Highlights • A novel incremental convex hull algorithm is proposed with O (h 2 ) time complexity. • The convex hull is maintained as a set of line segments. • The proposed algorithm is  ...  A three dimensional output sensitive algorithm was invented with optimal time complexity (Charkson and Shor, 1989) .  ... 
doi:10.4038/cjs.v50i3.7907 fatcat:ixepocfthbethn3gofbtve4kfq

Algorithms for Mining Association Rules for Binary Segmentations of Huge Categorical Databases

Yasuhiko Morimoto, Takeshi Fukuda, Hirofumi Matsuzawa, Takeshi Tokuyama, Kunikazu Yoda
1998 Very Large Data Bases Conference  
However, when the objective function is convex, there are feasible algorithms for finding nearly optimal binary segmentations, and we prove that typical criteria, such as "entropy (mutual information),  ...  The optimality of segmentation is defined by an objective function suitable for the user's objective.  ...  Those trials are executed independently and in parallel; thus, the Random Algorithm is suitable for a parallel environment.  ... 
dblp:conf/vldb/MorimotoFMTY98 fatcat:jgvhha4buze6dhrkpddlbygrqm
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