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

1998
*
Lecture Notes in Computer Science
*

In 20 , Reif and Sen gave an

doi:10.1007/3-540-64359-1_714
fatcat:qaoirqoybrdtxh322pvryxjgxq
*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. ...##
###
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

2012
*
Computers & graphics
*

We present

doi:10.1016/j.cag.2012.03.015
fatcat:vjsmjtv4u5fi3kyvp7ayckvl4e
*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 ...##
###
A Randomized Parallel Three-Dimensional Convex Hull Algorithm for Coarse-Grained Multicomputers

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 ...

##
###
Parallel algorithms in geometry
[chapter]

2004
*
Handbook of Discrete and Computational Geometry, Second Edition
*

Is there an efficient output-sensitive

doi:10.1201/9781420035315.ch42
fatcat:bjv5rzaoxne5tjle6ppvondlam
*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 ...##
###
Maximum overlap and minimum convex hull of two convex polyhedra under translations

2008
*
Computational geometry
*

Given two

doi:10.1016/j.comgeo.2007.08.001
fatcat:n5uoshjeqfaixn7sd3wzu5opnm
*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*...##
###
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

2003
*
Journal of Parallel and Distributed Computing
*

In this paper we focus on the problem of designing very fast

doi:10.1016/s0743-7315(03)00035-2
fatcat:l27fsx5wb5alzhl2bv3lmgatdm
*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. ...##
###
Data Mining Analysis and High-dimensional Visualization Based on Electric Big Data

2017
*
DEStech Transactions on Engineering and Technology Research
*

through

doi:10.12783/dtetr/iceta2016/7057
fatcat:njivsiljerbzjhoqgmn57vdtl4
*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*...##
###
Polling: a new randomized sampling technique for computational geometry

1989
*
Proceedings of the twenty-first annual ACM symposium on Theory of computing - STOC '89
*

The best known deterministic

doi:10.1145/73007.73045
dblp:conf/stoc/ReifS89
fatcat:mtfext2ncrbtjlqu2hz4qokqsu
*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. ...##
###
A randomized parallel 3D convex hull algorithm for coarse grained multicomputers

1995
*
Proceedings of the seventh annual ACM symposium on Parallel algorithms and architectures - SPAA '95
*

We present

doi:10.1145/215399.215410
dblp:conf/spaa/DehneDDFK95
fatcat:is3euybf4nferah244bf4dq3ba
*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*. ...##
###
Convex hulls of finite sets of points in two and three dimensions

1977
*
Communications of the ACM
*

Since the

doi:10.1145/359423.359430
fatcat:rke3cem5grfpjkw5spk5rmp7i4
*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 ...##
###
An efficient planar incremental convex hull algorithm to find the edges of the boundary polygon of the convex hull of a set of points

2021
*
Ceylon Journal of Science
*

The

doi:10.4038/cjs.v50i3.7907
fatcat:ixepocfthbethn3gofbtve4kfq
*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) . ...##
###
Algorithms for Mining Association Rules for Binary Segmentations of Huge Categorical Databases

1998
*
Very Large Data Bases Conference
*

However, when the objective function is

dblp:conf/vldb/MorimotoFMTY98
fatcat:jgvhha4buze6dhrkpddlbygrqm
*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. ...
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