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An introduction to parallel algorithms

01 Oct 1992-
TL;DR: This book provides an introduction to the design and analysis of parallel algorithms, with the emphasis on the application of the PRAM model of parallel computation, with all its variants, to algorithm analysis.
Abstract: Written by an authority in the field, this book provides an introduction to the design and analysis of parallel algorithms. The emphasis is on the application of the PRAM (parallel random access machine) model of parallel computation, with all its variants, to algorithm analysis. Special attention is given to the selection of relevant data structures and to algorithm design principles that have proved to be useful. Features *Uses PRAM (parallel random access machine) as the model for parallel computation. *Covers all essential classes of parallel algorithms. *Rich exercise sets. *Written by a highly respected author within the field. 0201548569B04062001

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Citations
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Proceedings ArticleDOI
15 Mar 1995
TL;DR: This paper designs parallel algorithms in relation with the actual parallel machine models and shows the importance of integrating parallel algorithms with parallelMachine models.
Abstract: In teaching of Parallel Algorithms, emphasis is usually placed on algorithms that are based on parallel random access machine (PRAM) model, but those algorithms may or may not be efficiently implementable on real parallel machines. In this paper we design parallel algorithms in relation with the actual parallel machine models and show the importance of integrating parallel algorithms with parallel machine models. We discuss this approach using traveling salesperson problem (TSP) as an example.

8 citations


Cites methods from "An introduction to parallel algorit..."

  • ...However M parallel operations of summation and comparison can be parallelized on CREW model with a O(log?vt) complexity [ 4 ], where M is (n-1) !. Also, the algorithm makes use of M processors, which is a very large number when n gets larger....

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  • ...More practically by using the prefix summation and comparison algorithms[ 4 ], this algorithm can be run on CREW PR4M model in O(nlogn) time....

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Journal ArticleDOI
TL;DR: It is shown that some pairs of vertices in hypercubes with faulty edges can be connected even if n - 3 additional edges are faulty, and it is proved that no other Hamiltonian paths are possible.

8 citations

Proceedings ArticleDOI
20 Jul 1995
TL;DR: NC algorithms to achieve approximation factors of 3/2 + e for these two problems without computing depth-first-search trees are presented.
Abstract: Consider the following NP-hard problems: Given a graph G , find minimum 2-edge connected and 2-vertex connected subgraphs spanning all vertices of G . Over the past few years, exciting sequential algorithms for approximating such minimum subgraphs have been produced [6],[10]. The approximation factors are improved from 2 to 3/2 for both of the problems. Yet the techniques involved are all based on augmenting depth-first-search trees and no similar progress has been carried to the parallel context. This paper presents NC algorithms to achieve approximation factors of 3/2 + e for these two problems without computing depth-first-search trees.

8 citations

Journal Article
TL;DR: In this paper, the authors present a logarithmic-time and optimal linear-work parallel algorithm on the parallel random access machine model that finds all successive minimal maximum subsequences of a real-valued sequence.
Abstract: Efficient algorithms for finding multiple contiguous subsequences of a real-valued sequence having large cumulative sums, in addition to its combinatorial appeal, have widely varying applications such as in textual information retrieval and bioinformatics. A maximum contiguous subsequence of a real-valued sequence is a contiguous subsequence with the maximum cumulative sum. A minimal maximum contiguous subsequence is a minimal contiguous subsequence (with respect to subsequential containment) among all maximum ones of the sequence. We present a logarithmic-time and optimal linear-work parallel algorithm on the parallel random access machine model that finds all successive minimal maximum subsequences of a real-valued sequence.

8 citations

Proceedings Article
01 Jan 2011

8 citations

References
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Book
01 Sep 1991
TL;DR: This chapter discusses sorting on a Linear Array with a Systolic and Semisystolic Model of Computation, which automates the very labor-intensive and therefore time-heavy and expensive process of manually sorting arrays.
Abstract: Preface Acknowledgments Notation 1 Arrays and Trees 1.1 Elementary Sorting and Counting 1.1.1 Sorting on a Linear Array Assessing the Performance of the Algorithm Sorting N Numbers with Fewer Than N Processors 1.1.2 Sorting in the Bit Model 1.1.3 Lower Bounds 1.1.4 A Counterexample-Counting 1.1.5 Properties of the Fixed-Connection Network Model 1.2 Integer Arithmetic 1.2.1 Carry-Lookahead Addition 1.2.2 Prefix Computations-Segmented Prefix Computations 1.2.3 Carry-Save Addition 1.2.4 Multiplication and Convolution 1.2.5 Division and Newton Iteration 1.3 Matrix Algorithms 1.3.1 Elementary Matrix Products 1.3.2 Algorithms for Triangular Matrices 1.3.3 Algorithms for Tridiagonal Matrices -Odd-Even Reduction -Parallel Prefix Algorithms 1.3.4 Gaussian Elimination 1.3.5 Iterative Methods -Jacobi Relaxation -Gauss-Seidel Relaxation Finite Difference Methods -Multigrid Methods 1.4 Retiming and Systolic Conversion 1.4.1 A Motivating Example-Palindrome Recognition 1.4.2 The Systolic and Semisystolic Model of Computation 1.4.3 Retiming Semisystolic Networks 1.4.4 Conversion of a Semisystolic Network into a Systolic Network 1.4.5 The Special Case of Broadcasting 1.4.6 Retiming the Host 1.4.7 Design by Systolic Conversion-A Summary 1.5 Graph Algorithms 1.5.1 Transitive Closure 1.5.2 Connected Components 1.5.3 Shortest Paths 1.5.4 Breadth-First Spanning Trees 1.5.5 Minimum Weight Spanning Trees 1.6 Sorting Revisited 1.6.1 Odd-Even Transposition Sort on a Linear Array 1.6.2 A Simple Root-N(log N + 1)-Step Sorting Algorithm 1.6.3 A (3 Root- N + o(Root-N))-Step Sorting Algorithm 1.6.4 A Matching Lower Bound 1.7 Packet Routing 1.7.1 Greedy Algorithms 1.7.2 Average-Case Analysis of Greedy Algorithms -Routing N Packets to Random Destinations -Analysis of Dynamic Routing Problems 1.7.3 Randomized Routing Algorithms 1.7.4 Deterministic Algorithms with Small Queues 1.7.5 An Off-line Algorithm 1.7.6 Other Routing Models and Algorithms 1.8 Image Analysis and Computational Geometry 1.8.1 Component-Labelling Algorithms -Levialdi's Algorithm -An O (Root-N)-Step Recursive Algorithm 1.8.2 Computing Hough Transforms 1.8.3 Nearest-Neighbor Algorithms 1.8.4 Finding Convex Hulls 1.9 Higher-Dimensional Arrays 1.9.1 Definitions and Properties 1.9.2 Matrix Multiplication 1.9.3 Sorting 1.9.4 Packet Routing 1.9.5 Simulating High-Dimensional Arrays on Low-Dimensional Arrays 1.10 problems 1.11 Bibliographic Notes 2 Meshes of Trees 2.1 The Two-Dimensional Mesh of Trees 2.1.1 Definition and Properties 2.1.2 Recursive Decomposition 2.1.3 Derivation from KN,N 2.1.4 Variations 2.1.5 Comparison With the Pyramid and Multigrid 2.2 Elementary O(log N)-Step Algorithms 2.2.1 Routing 2.2.2 Sorting 2.2.3 Matrix-Vector Multiplication 2.2.4 Jacobi Relaxation 2.2.5 Pivoting 2.2.6 Convolution 2.2.7 Convex Hull 2.3 Integer Arithmetic 2.3.1 Multiplication 2.3.2 Division and Chinese Remaindering 2.3.3 Related Problems -Iterated Products -Rooting Finding 2.4 Matrix Algorithms 2.4.1 The Three-Dimensional Mesh of Trees 2.4.2 Matrix Multiplication 2.4.3 Inverting Lower Triangular Matrices 2.4.4 Inverting Arbitrary Matrices -Csanky's Algorithm -Inversion by Newton Iteration 2.4.5 Related Problems 2.5 Graph Algorithms 2.5.1 Minimum-Weight Spanning Trees 2.5.2 Connected Components 2.5.3 Transitive Closure 2.5.4 Shortest Paths 2.5.5 Matching Problems 2.6 Fast Evaluation of Straight-Line Code 2.6.1 Addition and Multiplication Over a Semiring 2.6.2 Extension to Codes with Subtraction and Division 2.6.3 Applications 2.7 Higher-Dimensional meshes of Trees 2.7.1 Definitions and Properties 2.7.2 The Shuffle-Tree Graph 2.8 Problems 2.9 Bibliographic Notes 3 Hypercubes and Related Networks 3.1 The Hypercube 3.1.1 Definitions and Properties 3.1.2 Containment of Arrays -Higher-Dimensional Arrays -Non-Power-of-2 Arrays 3.1.3 Containment of Complete Binary Trees 3.1.4 Embeddings of Arbitrary Binary Trees -Embeddings with Dilation 1 and Load O(M over N + log N) -Embeddings with Dilation O(1) and Load O (M over N + 1) -A Review of One-Error-Correcting Codes -Embedding Plog N into Hlog N 3.1.5 Containment of Meshes of Trees 3.1.6 Other Containment Results 3.2 The Butterfly, Cube-Connected-Cycles , and Benes Network 3.2.1 Definitions and Properties 3.2.2 Simulation of Arbitrary Networks 3.2.3 Simulation of Normal Hypercube Algorithms 3.2.4 Some Containment and Simulation Results 3.3 The Shuffle-Exchange and de Bruijn Graphs 3.3.1 Definitions and Properties 3.3.2 The Diaconis Card Tricks 3.3.3 Simulation of Normal Hypercube Algorithms 3.3.4 Similarities with the Butterfly 3.3.5 Some Containment and Simulation Results 3.4 Packet-Routing Algorithms 3.4.1 Definitions and Routing Models 3.4.2 Greedy Routing Algorithms and Worst-Case Problems 3.4.3 Packing, Spreading, and Monotone Routing Problems -Reducing a Many-to-Many Routing Problem to a Many-to-One Routing Problem -Reducing a Routing Problem to a Sorting Problem 3.4.4 The Average-Case Behavior of the Greedy Algorithm -Bounds on Congestion -Bounds on Running Time -Analyzing Non-Predictive Contention-Resolution Protocols 3.4.5 Converting Worst-Case Routing Problems into Average-Case Routing Problems -Hashing -Randomized Routing 3.4.6 Bounding Queue Sizes -Routing on Arbitrary Levelled Networks 3.4.7 Routing with Combining 3.4.8 The Information Dispersal Approach to Routing -Using Information Dispersal to Attain Fault-Tolerance -Finite Fields and Coding Theory 3.4.9 Circuit-Switching Algorithms 3.5 Sorting 3.5.1 Odd-Even Merge Sort -Constructing a Sorting Circuit with Depth log N(log N +1)/2 3.5.2 Sorting Small Sets 3.5.3 A Deterministic O(log N log log N)-Step Sorting Algorithm 3.5.4 Randomized O(log N)-Step Sorting Algorithms -A Circuit with Depth 7.45 log N that Usually Sorts 3.6 Simulating a Parallel Random Access Machine 3.6.1 PRAM Models and Shared Memories 3.6.2 Randomized Simulations Based on Hashing 3.6.3 Deterministic Simulations using Replicated Data 3.6.4 Using Information Dispersal to Improve Performance 3.7 The Fast Fourier Transform 3.7.1 The Algorithm 3.7.2 Implementation on the Butterfly and Shuffle-Exchange Graph 3.7.3 Application to Convolution and Polynomial Arithmetic 3.7.4 Application to Integer Multiplication 3.8 Other Hypercubic Networks 3.8.1 Butterflylike Networks -The Omega Network -The Flip Network -The Baseline and Reverse Baseline Networks -Banyan and Delta Networks -k-ary Butterflies 3.8.2 De Bruijn-Type Networks -The k-ary de Bruijn Graph -The Generalized Shuffle-Exchange Graph 3.9 Problems 3.10 Bibliographic Notes Bibliography Index Lemmas, Theorems, and Corollaries Author Index Subject Index

2,895 citations


"An introduction to parallel algorit..." refers background in this paper

  • ...Multiprocessorbased computers have been around for decades and various types of computer architectures [2] have been implemented in hardware throughout the years with different types of advantages/performance gains depending on the application....

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  • ...Every location in the array represents a node of the tree: T [1] is the root, with children at T [2] and T [3]....

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  • ...The text by [2] is a good start as it contains a comprehensive description of algorithms and different architecture topologies for the network model (tree, hypercube, mesh, and butterfly)....

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Book
01 Jan 1984
TL;DR: The authors have divided the use of computers into the following four levels of sophistication: data processing, information processing, knowledge processing, and intelligence processing.
Abstract: The book is intended as a text to support two semesters of courses in computer architecture at the college senior and graduate levels. There are excellent problems for students at the end of each chapter. The authors have divided the use of computers into the following four levels of sophistication: data processing, information processing, knowledge processing, and intelligence processing.

1,410 citations


"An introduction to parallel algorit..." refers background in this paper

  • ...Parallel architectures have been described in several books (see, for example, [18, 29])....

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Journal ArticleDOI
TL;DR: The success of data parallel algorithms—even on problems that at first glance seem inherently serial—suggests that this style of programming has much wider applicability than was previously thought.
Abstract: Parallel computers with tens of thousands of processors are typically programmed in a data parallel style, as opposed to the control parallel style used in multiprocessing. The success of data parallel algorithms—even on problems that at first glance seem inherently serial—suggests that this style of programming has much wider applicability than was previously thought.

1,000 citations


"An introduction to parallel algorit..." refers background in this paper

  • ...Recent work on the mapping of PRAM algorithms on bounded-degree networks is described in [3,13,14, 20, 25], Our presentation on the communication complexity of the matrix-multiplication problem in the sharedmemory model is taken from [1], Data-parallel algorithms are described in [15]....

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Proceedings ArticleDOI
01 May 1978
TL;DR: A model of computation based on random access machines operating in parallel and sharing a common memory is presented and can accept in polynomial time exactly the sets accepted by nondeterministic exponential time bounded Turing machines.
Abstract: A model of computation based on random access machines operating in parallel and sharing a common memory is presented. The computational power of this model is related to that of traditional models. In particular, deterministic parallel RAM's can accept in polynomial time exactly the sets accepted by polynomial tape bounded Turing machines; nondeterministic RAM's can accept in polynomial time exactly the sets accepted by nondeterministic exponential time bounded Turing machines. Similar results hold for other classes. The effect of limiting the size of the common memory is also considered.

951 citations


"An introduction to parallel algorit..." refers background in this paper

  • ...Rigorous descriptions of shared-memory models were introduced later in [11,12]....

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Journal ArticleDOI
TL;DR: It is shown that arithmetic expressions with n ≥ 1 variables and constants; operations of addition, multiplication, and division; and any depth of parenthesis nesting can be evaluated in time 4 log 2 + 10(n - 1) using processors which can independently perform arithmetic operations in unit time.
Abstract: It is shown that arithmetic expressions with n ≥ 1 variables and constants; operations of addition, multiplication, and division; and any depth of parenthesis nesting can be evaluated in time 4 log2n + 10(n - 1)/p using p ≥ 1 processors which can independently perform arithmetic operations in unit time. This bound is within a constant factor of the best possible. A sharper result is given for expressions without the division operation, and the question of numerical stability is discussed.

864 citations


"An introduction to parallel algorit..." refers methods in this paper

  • ...The WT scheduling principle is derived from a theorem in [7], In the literature, this principle is commonly referred to as Brent's theorem or Brent's scheduling principle....

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