Book•
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
Citations
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05 Jul 2010
TL;DR: This paper presents a framework for parallelizing service composition algorithms investigating how to partition the composition problem into multiple parallel threads, and proposes two novel approaches to evenly distribute the workload in a sophisticated fashion.
Abstract: Data intensive applications, e.g. in life sciences, pose new efficiency challenges to the service composition problem. Since today computing power is mainly increased by multiplication of CPU cores, algorithms have to be redesigned to benefit from this evolution. In this paper we present a framework for parallelizing service composition algorithms investigating how to partition the composition problem into multiple parallel threads. But in contrast to intuition, the straightforward parallelization techniques do not lead to superior performance as our baseline evaluation reveals. To harness the full power of multicore architectures, we propose two novel approaches to evenly distribute the workload in a sophisticated fashion. In fact, our extensive experiments on practical life science data resulted in an impressive speedup of over 300% using only 4 cores. Moreover, we show that our techniques can also benefit from all advanced pruning heuristics used in sequential algorithms.
50 citations
13 Jun 2015
TL;DR: This work implements the parallel integer sorting algorithm of Rajasekaran and Reif, but instead of processing bits of a integers in a reduced range in a bottom-up fashion, it process the hashed values of keys directly top-down.
Abstract: Semisorting is the problem of reordering an input array of keys such that equal keys are contiguous but different keys are not necessarily in sorted order. Semisorting is important for collecting equal values and is widely used in practice. For example, it is the core of the MapReduce paradigm, is a key component of the database join operation, and has many other applications. We describe a (randomized) parallel algorithm for the problem that is theoretically efficient (linear work and logarithmic depth), but is designed to be more practically efficient than previous algorithms. We use ideas from the parallel integer sorting algorithm of Rajasekaran and Reif, but instead of processing bits of a integers in a reduced range in a bottom-up fashion, we process the hashed values of keys directly top-down. We implement the algorithm and experimentally show on a variety of input distributions that it outperforms a similarly-optimized radix sort on a modern 40-core machine with hyper-threading by about a factor of 1.7--1.9, and achieves a parallel speedup of up to 38x. We discuss the various optimizations used in our implementation and present an extensive experimental analysis of its performance.
50 citations
Cites methods from "An introduction to parallel algorit..."
...We use the work-depth model [13] allowing for concurrent reads and writes, where work W is equal to the number of operations required (equivalently, the product of the time and the number of processors) and depth (span) D is equal to the number of time steps required....
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15 Apr 1996
TL;DR: Efficient and portable implementations of a useful image enhancement process, the symmetric neighborhood filter (SNF), and an image segmentation technique which makes use of the SNF and a variant of the conventional connected components algorithm which is called /spl delta/-connected components.
Abstract: Presents efficient and portable implementations of a useful image enhancement process, the symmetric neighborhood filter (SNF), and an image segmentation technique which makes use of the SNF and a variant of the conventional connected components algorithm which we call /spl delta/-connected components. We use efficient techniques for distributing and coalescing data as well as efficient combinations of task and data parallelism. The image segmentation algorithm makes use of an efficient connected components algorithm based on a novel approach for parallel merging. The algorithms have been coded in Split-C and run on a variety of platforms, including the Thinking Machines CM-5, IBM SP-1 and SP-2, Cray Research T3D, Meiko Scientific CS-2, Intel Paragon, and workstation clusters. Our experimental results are consistent with the theoretical analysis (and provide the best known execution times for segmentation, even when compared with machine-specific implementations). Our test data include difficult images from the Landsat Thematic Mapper (TM) satellite data.
50 citations
TL;DR: The parallel watershed transformation used in gray-scale image segmentation is here augmented to perform with the aid of a priori supplied image cues called markers to calibrate a resilient algorithm to oversegmentation.
50 citations
Cites background or methods from "An introduction to parallel algorit..."
...For the image example in Fig. 1a, the subimages of labels o after the local watershed are illustrated in Fig. 5. The BCG for every processor in 8-connectivity is bcg0= [[2, 5], [0, 5], [1, 8], [0, 9], [0, 7], [0, 11], [4, 6]], bcg1=[ [6, 4], [5, 2], [5, 0], [5, 12], [6, 13]], bcg2=[[9, 0], [ 7 , 0], [10, 13], [8, 1]], bcg3=[[11, 0], [12, 5], [13, 6], [13, 10]]....
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...For the same reason, vertices [5, 6], [ 7 , 8, 9, 10], and [11, 12, 13] are unsolved in the processors they belong to....
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...Several parallel implementations of the Boru# vka algorithm exist in the literature [5, 7 , 9, 21], but for our problem, we need a constrained parallel MSF operator....
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...For the image example in Fig. 1a, the subimages of labels o after the local watershed are illustrated in Fig. 5. The BCG for every processor in 8-connectivity is bcg0= [[2, 5], [0, 5], [1, 8], [0, 9], [0, 7 ], [0, 11], [4, 6]], bcg1=[ [6, 4], [5, 2], [5, 0], [5, 12], [6, 13]], bcg2=[[9, 0], [7, 0], [10, 13], [8, 1]], bcg3=[[11, 0], [12, 5], [13, 6], [13, 10]]....
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28 Jan 1996
TL;DR: In this article, the first randomized O(log n) time and O(m + n) work EREW PRAM algorithm for finding a spanning forest of an undirected graph G = (V, E) with n vertices and m edges was presented.
Abstract: We present the first randomized O(log n) time and O(m + n) work EREW PRAM algorithm for finding a spanning forest of an undirected graph G = (V, E) with n vertices and m edges. Our algorithm is optimal with respect to time, work and space. As a consequence we get optimal randomized EREW PRAM algorithms for other basic connectivity problems such as finding a bipartite partition, finding bridges and biconnected components, and finding Euler tours in Eulerean graphs. For other problems such as finding an ear decomposition, finding an open ear decomposition, finding a strong orientation, and finding an st-numbering we get optimal randomized CREW PRAM algorithms.
49 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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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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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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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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