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Optimal parallel algorithms for computing convex hulls and for sorting

Byline: S. G. Akl (1) Keywords: B.3.2. [Memory Structures]: Design Styles -- shared memory; C.1.2. [Computer Systems Organization]: Multiple Data Stream Architectures (Multi-Processors) --single-instruction-stream, multiple-data-stream processors (SIMD); F.2.2., F.2.3. [Analysis of Algorithms and Pr... Full description

Journal Title: Computing 1984, Vol.33 (1), p.1-11
Main Author: AKL, S. G
Format: Electronic Article Electronic Article
Language: English
Subjects:
Publisher: Wien: Springer
ID: ISSN: 0010-485X
Link: http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=8988735
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recordid: cdi_gale_infotracacademiconefile_A153918392
title: Optimal parallel algorithms for computing convex hulls and for sorting
format: Article
creator:
  • AKL, S. G
subjects:
  • Algorithmics. Computability. Computer arithmetics
  • Algorithms
  • Analysis
  • Applied sciences
  • Computer science
  • control theory
  • systems
  • Exact sciences and technology
  • Theoretical computing
ispartof: Computing, 1984, Vol.33 (1), p.1-11
description: Byline: S. G. Akl (1) Keywords: B.3.2. [Memory Structures]: Design Styles -- shared memory; C.1.2. [Computer Systems Organization]: Multiple Data Stream Architectures (Multi-Processors) --single-instruction-stream, multiple-data-stream processors (SIMD); F.2.2., F.2.3. [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems -- computations on discrete structures, geometrical problems and computations, sorting and searching: Trade-offs among Complexity Measures; Convex hull; median; parallel algorithm; selection A parallel algorithm is presented for computing the convex hull of a set ofn points in the plane. The algorithm usesn .sup.1-[epsilon] processors, 0
language: eng
source:
identifier: ISSN: 0010-485X
fulltext: no_fulltext
issn:
  • 0010-485X
  • 1436-5057
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titleOptimal parallel algorithms for computing convex hulls and for sorting
creatorAKL, S. G
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descriptionByline: S. G. Akl (1) Keywords: B.3.2. [Memory Structures]: Design Styles -- shared memory; C.1.2. [Computer Systems Organization]: Multiple Data Stream Architectures (Multi-Processors) --single-instruction-stream, multiple-data-stream processors (SIMD); F.2.2., F.2.3. [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems -- computations on discrete structures, geometrical problems and computations, sorting and searching: Trade-offs among Complexity Measures; Convex hull; median; parallel algorithm; selection A parallel algorithm is presented for computing the convex hull of a set ofn points in the plane. The algorithm usesn .sup.1-[epsilon] processors, 0<[epsilon]<1, and runs inO(n .sup.[epsilon] logh) time, whereh is the number of edges on the convex hull, for a total cost ofO (n logh). This performance matches that of the best currently known sequential convex hull algorithm. In addition, sinceha$?n, the algorithm is worst-case optimal in view of the [OMEGA] (n logn) worst-case lower bound on sequential convex hull computation. It is also shown that the convex hull algorithm leads to a parallel sorting algorithm whose total cost isO(n logn), which is optimal. (German): In dieser Arbeit wird ein paralleler Algorithmus zur Berechnung der konvexen Hulle einer Menge vonn Punkten in der Ebene vorgestellt. Der Algorithmus benotigtn .sup.1-[epsilon] Prozessoren, 0<[epsilon]<1, und lauft in der ZeitO(n .sup.[epsilon] logh), wobeih die Zahl der Kanten der konvexen Hulle ist. Daraus ergeben sich Gesamtkosten vonO(n logh). Dieses Verhalten stimmt mit dem des besten bisher bekannten sequentiellen Algorithmus zur Berechnung der konvexen Hulle uberein. Der Algorithmus ist zusatzlich optimal im schlechtesten Fall, daha$?n gilt und [OMEGA](n logn) eine untere Schranke fur die sequentielle Berechnung der konvexen Hulle ist. Ausserdem wird gezeigt, dass der Algorithmus fur die konvexe Hulle zu einem parallelen Sortierverfahren fuhrt, dessen GesamtkostenO(n logn) sind, d. h. auch dieses Verfahren ist optimal. Author Affiliation: (1) Department of Computing and Information Science, Queen's University, K7L 3N6, Kingston, Canada Article History: Registration Date: 19/10/2005 Received Date: 22/09/1983 Article note: This work was supported by the Natural Sciences and Engineering Research Council of Canada under grant NSERC-A3336.
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descriptionByline: S. G. Akl (1) Keywords: B.3.2. [Memory Structures]: Design Styles -- shared memory; C.1.2. [Computer Systems Organization]: Multiple Data Stream Architectures (Multi-Processors) --single-instruction-stream, multiple-data-stream processors (SIMD); F.2.2., F.2.3. [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems -- computations on discrete structures, geometrical problems and computations, sorting and searching: Trade-offs among Complexity Measures; Convex hull; median; parallel algorithm; selection A parallel algorithm is presented for computing the convex hull of a set ofn points in the plane. The algorithm usesn .sup.1-[epsilon] processors, 0<[epsilon]<1, and runs inO(n .sup.[epsilon] logh) time, whereh is the number of edges on the convex hull, for a total cost ofO (n logh). This performance matches that of the best currently known sequential convex hull algorithm. In addition, sinceha$?n, the algorithm is worst-case optimal in view of the [OMEGA] (n logn) worst-case lower bound on sequential convex hull computation. It is also shown that the convex hull algorithm leads to a parallel sorting algorithm whose total cost isO(n logn), which is optimal. (German): In dieser Arbeit wird ein paralleler Algorithmus zur Berechnung der konvexen Hulle einer Menge vonn Punkten in der Ebene vorgestellt. Der Algorithmus benotigtn .sup.1-[epsilon] Prozessoren, 0<[epsilon]<1, und lauft in der ZeitO(n .sup.[epsilon] logh), wobeih die Zahl der Kanten der konvexen Hulle ist. Daraus ergeben sich Gesamtkosten vonO(n logh). Dieses Verhalten stimmt mit dem des besten bisher bekannten sequentiellen Algorithmus zur Berechnung der konvexen Hulle uberein. Der Algorithmus ist zusatzlich optimal im schlechtesten Fall, daha$?n gilt und [OMEGA](n logn) eine untere Schranke fur die sequentielle Berechnung der konvexen Hulle ist. Ausserdem wird gezeigt, dass der Algorithmus fur die konvexe Hulle zu einem parallelen Sortierverfahren fuhrt, dessen GesamtkostenO(n logn) sind, d. h. auch dieses Verfahren ist optimal. Author Affiliation: (1) Department of Computing and Information Science, Queen's University, K7L 3N6, Kingston, Canada Article History: Registration Date: 19/10/2005 Received Date: 22/09/1983 Article note: This work was supported by the Natural Sciences and Engineering Research Council of Canada under grant NSERC-A3336.
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abstractByline: S. G. Akl (1) Keywords: B.3.2. [Memory Structures]: Design Styles -- shared memory; C.1.2. [Computer Systems Organization]: Multiple Data Stream Architectures (Multi-Processors) --single-instruction-stream, multiple-data-stream processors (SIMD); F.2.2., F.2.3. [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems -- computations on discrete structures, geometrical problems and computations, sorting and searching: Trade-offs among Complexity Measures; Convex hull; median; parallel algorithm; selection A parallel algorithm is presented for computing the convex hull of a set ofn points in the plane. The algorithm usesn .sup.1-[epsilon] processors, 0<[epsilon]<1, and runs inO(n .sup.[epsilon] logh) time, whereh is the number of edges on the convex hull, for a total cost ofO (n logh). This performance matches that of the best currently known sequential convex hull algorithm. In addition, sinceha$?n, the algorithm is worst-case optimal in view of the [OMEGA] (n logn) worst-case lower bound on sequential convex hull computation. It is also shown that the convex hull algorithm leads to a parallel sorting algorithm whose total cost isO(n logn), which is optimal. (German): In dieser Arbeit wird ein paralleler Algorithmus zur Berechnung der konvexen Hulle einer Menge vonn Punkten in der Ebene vorgestellt. Der Algorithmus benotigtn .sup.1-[epsilon] Prozessoren, 0<[epsilon]<1, und lauft in der ZeitO(n .sup.[epsilon] logh), wobeih die Zahl der Kanten der konvexen Hulle ist. Daraus ergeben sich Gesamtkosten vonO(n logh). Dieses Verhalten stimmt mit dem des besten bisher bekannten sequentiellen Algorithmus zur Berechnung der konvexen Hulle uberein. Der Algorithmus ist zusatzlich optimal im schlechtesten Fall, daha$?n gilt und [OMEGA](n logn) eine untere Schranke fur die sequentielle Berechnung der konvexen Hulle ist. Ausserdem wird gezeigt, dass der Algorithmus fur die konvexe Hulle zu einem parallelen Sortierverfahren fuhrt, dessen GesamtkostenO(n logn) sind, d. h. auch dieses Verfahren ist optimal. Author Affiliation: (1) Department of Computing and Information Science, Queen's University, K7L 3N6, Kingston, Canada Article History: Registration Date: 19/10/2005 Received Date: 22/09/1983 Article note: This work was supported by the Natural Sciences and Engineering Research Council of Canada under grant NSERC-A3336.
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