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
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Posted Content•
TL;DR: This survey is an attempt to formalize the intuitive notion of "behavioral complexity" that one easily observes in simulations, namely, the complexity of knowing, given a finite configuration and a cell in c, if cell x will eventually become unstable.
Abstract: Since their introduction in the 80s, sandpile models have raised interest for their simple definition and their surprising dynamical properties. In this survey we focus on the computational complexity of the prediction problem, namely, the complexity of knowing, given a finite configuration $c$ and a cell $x$ in $c$, if cell $x$ will eventually become unstable. This is an attempt to formalize the intuitive notion of "behavioral complexity" that one easily observes in simulations. However, despite many efforts and nice results, the original question remains open: how hard is it to predict the two-dimensional sandpile model of Bak, Tang and Wiesenfeld?
3 citations
Cites background or methods from "An introduction to parallel algorit..."
...made progress in various directions to capture the essence of P-completeness in majority cellular automata [33, 36, 37, 38, 39], with notable applications of NC algorithms from [43]....
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...For more details, the reader is referred to [40, 43, 60]....
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Posted Content•
TL;DR: This paper presents a package of generic sequential and parallel algorithms for computationally and memory efficient HOS estimations which can be employed on any parallel machine or platform and implements the algorithms for both bispectrum and trispectrum estimations.
Abstract: Polyspectral estimation is a problem of great importance in the analysis of nonlinear time series that has applications in biomedical signal processing, communications, geophysics, image, radar, sonar and speech processing, etc. Higher order spectra (HOS) have been used in unsupervised and supervised clustering in big data scenarios, in testing for Gaussianity, to suppress Gaussian noise, to characterize nonlinearities in time series data, and so on .
Any algorithm for computing the $k$th order spectra of a time series of length $n$ needs $\Omega(n^{k-1})$ time since the output size will be $\Omega(n^{k-1})$ as well. Given that we live in an era of big data, $n$ could be very large. In this case, sequential algorithms might take unacceptable amounts of time. Thus it is essential to develop parallel algorithms. There is also room for improving existing sequential algorithms. In addition, parallel algorithms in the literature are nongeneric. In this paper we offer generic sequential algorithms for computing higher order spectra that are asymptotically faster than any published algorithm for HOS. Further, we offer memory efficient algorithms. We also present optimal parallel implementations of these algorithms on parallel computing models such as the PRAM and the mesh. We provide experimental results on our sequential and parallel algorithms. Our parallel implementation achieves very good speedups.
3 citations
Journal Article•
TL;DR: An algorithm of the parallelization of Iterative Dynamic Programming by the `Parallel Virtual Machine´ (PVM) language is described and it will be demonstrated that the parallelizing can lead to a considerable reduction in computing time.
Abstract: The present paper describes an algorithm of the parallelization of
Iterative Dynamic Programming by the `Parallel Virtual Machine´
(PVM) language. It will be demonstrated that the parallelization
can lead to a considerable reduction in computing time.
3 citations
01 Jan 2005
TL;DR: This paper describes an area-efficient architecture and algorithm for the evaluation of arithmetic expressions that effectively hides the pipeline latency of the floating-point cores and uses only onefloating-point core for each type of operator in the expression.
Abstract: Due to technological advances,it has becomepossible to implement floating-point coreson FPGAs in an effort to provide hardware acceleration for the myriad applications that require high performance floating-point arithmetic. However, in order to achieve a high clock rate, these floating-point cores must be deeply pipelined. Due to this deep pipelining and the complexity of floating-point arithmetic, floating-point cores use a great deal of the FPGA’s area. It is thus important to use as few floating-point cores in an architecture as possible.However, the deep pipelining makes it difficult to reusethe samefloatingpoint core for a series of floating-point computations that are dependent upon one another. In this paper, we describe an area-efficient architecture and algorithm for the evaluation of arithmetic expressions.This design effectively hides the pipeline latencyof the floating-point coresand usesonly onefloating-point core for each type of operator in the expression.The design is applicable to a wide variety of fields suchasscientific computing, cognition, and graph theory. We analyzethe performance of this design when implemented on a Xilinx Virtex-II Pro FPGA.
3 citations
Cites background or methods from "An introduction to parallel algorit..."
...To allow this partial evaluation, extra labels are applied to the tree nodes and the rake operation is augmented to handle the partial evaluation [ 12 ]....
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...These techniques employ tree contraction [ 12 ]....
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...[ 12 ], on the other hand, describes ways to transform into binary trees those...
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30 Mar 1998
TL;DR: Two parallel algorithms are presented, the direct algorithm and the split algorithm, for vector prefix and reduction computation on coarse-grained, distributed-memory parallel machines, and Experimental results on the CM-5 are presented.
Abstract: Vector prefix and reduction are collective communication primitives in which all processors must cooperate The authors present two parallel algorithms, the direct algorithm and the split algorithm, for vector prefix and reduction computation on coarse-grained, distributed-memory parallel machines The algorithms are relatively architecture independent and can be used effectively in many applications such as pack/unpack, array prefix/reduction functions, and array combining scatter functions, which are defined in Fortran 90 and in High Performance Fortran Experimental results on the CM-5 are presented
3 citations
Cites background from "An introduction to parallel algorit..."
...Z,. Then, at each level of an FBT (from 0 to d - l), each node A with the current value F(A) contributes the values of its two children as follows [2, 7 ,9]:...
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...Under the assumption that P is a power of two, in the split algorithm P full binary trees (FBT) of depth lg P are embedded to P processors, and then €' reduction or prefix is simultaneously performed on the P FBTs of depth lg P [2, 7 ] When M = Q(lg P), the split algorithm is cost optimal....
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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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