Parallel Sorting Algorithms

Parallel Sorting Algorithms

1st Edition - September 10, 1985

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  • Author: Selim G. Akl
  • eBook ISBN: 9781483268088

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Parallel Sorting Algorithms explains how to use parallel algorithms to sort a sequence of items on a variety of parallel computers. The book reviews the sorting problem, the parallel models of computation, parallel algorithms, and the lower bounds on the parallel sorting problems. The text also presents twenty different algorithms, such as linear arrays, mesh-connected computers, cube-connected computers. Another example where algorithm can be applied is on the shared-memory SIMD (single instruction stream multiple data stream) computers in which the whole sequence to be sorted can fit in the respective primary memories of the computers (random access memory), or in a single shared memory. SIMD processors communicate through an interconnection network or the processors communicate through a common and shared memory. The text also investigates the case of external sorting in which the sequence to be sorted is bigger than the available primary memory. In this case, the algorithms used in external sorting is very similar to those used to describe internal sorting, that is, when the sequence can fit in the primary memory, The book explains that an algorithm can reach its optimum possible operating time for sorting when it is running on a particular set of architecture, depending on a constant multiplicative factor. The text is suitable for computer engineers and scientists interested in parallel algorithms.

Table of Contents

  • Preface ix

    1. Introduction

    1.1 Motivation

    1.2 The Sorting Problem

    1.3 Parallel Models of Computation

    1.4 Parallel Algorithms

    1.5 Lower Bounds on the Parallel Sorting Problem

    1.6 Organization of the Book

    1.7 Bibliographical Remarks


    2. Networks for Sorting

    2.1 Introduction

    2.2 Enumeration Sort

    2.3 Sorting by Odd-Even Merging

    2.4 Sorting Based on Bitonic Merging

    2.5 Bibliographical Remarks


    3. Linear Arrays

    3.1 Introduction

    3.2 Odd-Even Transposition Sort

    3.3 Merge-Splitting Sort

    3.4 Mergesort on a Pipeline

    3.5 Enumeration Sort

    3.6 Bibliographical Remarks


    4. The Perfect Shuffle

    4.1 Introduction

    4.2 Bitonic Sorting Using the Perfect Shuffle

    4.3 An Optimal Merge-Splitting Algorithm

    4.4 Bibliographical Remarks


    5. Mesh-Connected Computers

    5.1 Introduction

    5.2 Model of Computation

    5.3 The Sorting Problem

    5.4 A Lower Bound

    5.5 Sorting on the Mesh

    5.6 An Optimal Algorithm

    5.7 Bibliographical Remarks


    6. Tree Machines

    6.1 Introduction

    6.2 Minimum Extraction

    6.3 Bucket Sorting and Merging

    6.4 Median Finding and Splitting

    6.5 Bibliographical Remarks


    7. Cube-Connected Computers

    7.1 Introduction

    7.2 Model of Computation

    7.3 The Sorting Problem

    7.4 The Sorting Machine

    7.5 Sorting on the Cube

    7.6 Bibliographical Remarks


    8. Shared-Memory SIMD Computers

    8.1 Introduction

    8.2 Model of Computation

    8.3 A Parallel Algorithm for Selection

    8.4 Sorting on a Shared-Memory SIMD Computer

    8.5 Bibliographical Remarks


    9. Asynchronous Sorting on Multiprocessors

    9.1 Introduction

    9.2 Running Asynchronous Algorithms

    9.3 Asynchronous Sorting by Enumeration

    9.4 Asynchronous Quicksort

    9.5 Bibliographical Remarks


    10. Parallel External Sorting

    10.1 Introduction

    10.2 External Sorting on a Tree

    10.3 External Sorting on a Pipeline

    10.4 Bibliographical Remarks


    11. Lower Bounds

    11.1 Introduction

    11.2 A Review of Lower Bounds

    11.3 Counting Comparisons

    11.4 Broadcasting

    11.5 A Lower Bound on Tree Sorting

    11.6 Bibliographical Remarks


    Author Index

    Subject Index

Product details

  • No. of pages: 244
  • Language: English
  • Copyright: © Academic Press 1985
  • Published: September 10, 1985
  • Imprint: Academic Press
  • eBook ISBN: 9781483268088

About the Author

Selim G. Akl

About the Editor

Werner Rheinboldt

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