Parallel Algorithms for Regular Architectures

by Miller, Russ; Stout, Quentin F.

• ISBN13: 9780262515542
• ISBN10: 0262515547
• Format: Paperback
• Copyright: 1996-09-01
• Publisher: Mit Pr

Summary

Parallel-Algorithms for Regular Architecturesis the first book to concentrate exclusively on algorithms and paradigms for programming parallel computers such as the hypercube, mesh, pyramid, and mesh-of-trees. Algorithms are given to solve fundamental tasks such as sorting and matrix operations, as well as problems in the field of image processing, graph theory, and computational geometry. The first chapter defines the computer models, problems to be solved, and notation that will be used throughout the book. It also describes fundamental abstract data movement operations that serve as the foundation to many of the algorithms presented in the book. The remaining chapters describe efficient implementations of these operations for specific models of computation and present algorithms (with asymptotic analyses) that are often based on these operations. The algorithms presented are the most efficient known, including a number of new algorithms for the hypercube and mesh-of-trees that are better than those that have previously appeared in the literature. The chapters may be read independently, allowing anyone interested in a specific model to read the introduction and then move directly to the chapter(s) devoted to the particular model of interest. Russ Miller is Assistant Professor in the Department of Computer Science, State University of New York at Buffalo. Quentin F. Stout is Associate Professor in the Department of Electrical Engineering and Computer Science at the University of Michigan. Parallel Algorithms for Regular Architecturesis included in the Scientific Computation series, edited by Dennis Gannon.

Table of Contents

Meshes and Pyramids

List of Figures

Preface

Overview of Chapters

Recommended Use

Correspondence

Acknowledgments

Overview

Introduction

Models of Computation

Preliminaries

Classification Schemes

Mesh Computer

Pyramid Computer

Mesh-of-Trees Architecture

Hypercube

Pram

Forms of Input

Problems

Graph and Image Problems

Computational Geometry Problems

Data Movement Operations

Sample Algorithms

Component Labeling for Digitized Picture Input

Convex Hull for Planar Point Data Input

Further Remarks

Fundamental Mesh Algorithms

Introduction

Definitions

Lower Bounds

Primitive Mesh Algorithms

Row and Column Rotations

Passing a Row (Column) Through the Mesh

Semigroup Operations, Reporting, and Broadcasting

Parallel Prefix

Matrix Algorithms

Matrix Transposition

Matrix Multiplication

Transitive Closure

Matrix Inverse

Algorithms Involving Ordered Data

Sorting

Rotating Data within Intervals

Semigroup Computation within Intervals

Concurrent Read and Concurrent Write

Compression

Further Remarks

Mesh Algorithms for Images and Graphs

Introduction

Fundamental Graph Algorithms

Bridge Edges

Articulation Points

Minimum Spanning Tree

Connected Components

Counting Connected Components

Labeling Connected Components

Internal Distances

Convexity

External Distances

Further Remarks

Mesh Algorithms for Computational Geometry

Introduction

Preliminaries

Initial Conditions

Lower Bounds

Fundamental Operations on the Mesh

The Convex Hull

Smallest Enclosing Figures

Nearest Point Problems

Line Segments and Simple Polygons

Intersection of Convex Sets

Diameter

Iso-oriented Rectangles and Polygons

Voronoi Diagram

Algorithm

Applications

Further Remarks

Tree-like Pyramid Algorithms

Introduction

Definitions

Lower Bounds

Fundamental Algorithms

Initializing Identity Registers

Bit Counting Problems

Computing Commutative Associative Binary Functions

Point Queries

Image Algorithms

Convexity Properties

Digitized Straight Line Segments

Further Remarks

Hybrid Pyramid Algorithms

Introduction

Graphs as Unordered Edges

Data Movement Operations

Component Labeling

Minimal Spanning Forests

Graphs as Adjacency Matrices

Data Movement Operations

Component Labeling and Minimal Spanning Forests

Digitized Pictures

Data Movement Operations

Component Labeling

Nearest Neighbors

Convexity

Data Movement Operations

Enumerating Extreme Points

Applications of Extreme Points

Data Movement Operations

Pyramid Read, Pyramid Write, and Count_keys

Pyramid Matrix Read and Pyramid Matrix Write

Funnel Read and Reducing a Function

Optimality

Further Remarks

Order Notation

Recurrence Equations

Bibliography

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