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
More filters
16 Nov 2004
TL;DR: A novel constant execution time barrier synchronization mechanism for scalable ESMMs using active memory that is applied to the Eclipse network-on-chip architecture and evaluated briefly.
Abstract: Explicit synchronization mechanisms capable of arbitrary simultaneous barriers are needed to support parallely recursive synchronous MIMD programming, even in step synchronous emulated shared memory machines (ESMM) because control of threads may privately depend on input values. Current synchronization mechanisms fail to support arbitrary simultaneous barriers or are not scalable with future silicon technologies. In this paper, we propose a novel constant execution time barrier synchronization mechanism for scalable ESMMs using active memory. The mechanism is applied to our Eclipse network-on-chip architecture and evaluated briefly.
2 citations
30 Sep 1993
TL;DR: An algorithm for the maximum empty rectangle problem is presented, which is work optimal in the expected case.
Abstract: We present optimal parallel solutions to direct dominance problems for planar point sets. Our algorithms are deterministic and designed to run on the concurrent read exclusive write parallel random-access machine (CREW PRAM). In particular, we provide algorithms for counting the number of points that are directly dominated by each point of a planar point set, and for reporting these point sets. The counting algorithm runs in O(log n) time using O(n) processors; the reporting algorithm runs in O(log n) time using O(n+k/log n) processors, where k is the size of the output. The total work of each algorithm matches the respective sequential lower bound. As an application of our results, we present an algorithm for the maximum empty rectangle problem, which is work optimal in the expected case.
2 citations
14 May 2000
TL;DR: A BSP-based parallel simplex method algorithm is introduced and its computational cost is analyzed, followed by some experimental results on a PC cluster and some conclusions are drawn.
Abstract: We introduce a BSP-based parallel simplex method algorithm and analyze its computational cost. Then we give some experimental results on a PC cluster and draw some conclusions.
2 citations
01 Feb 2010
TL;DR: This chapter is an introduction to the area of parallel computation written in accordance with the guidelines for the CRC HANDBOOK on algorithms and theory of computing where it will appear.
Abstract: This chapter is an introduction to the area of parallel computation written in accordance with the guidelines for the CRC HANDBOOK ON ALGORITHMS AND THEORY OF COMPUTATION where it will appear. References to chapters refer to other chapters in this book.
2 citations
Posted Content•
TL;DR: This paper studies the family of two-state Totalistic Freezing Cellular Automata defined over the triangular and square grids with von Neumann neighborhoods and exploits the properties of the automata in each group to show that the Stability problem is in $\text{NC}$.
Abstract: In this paper we study the family of two-state Totalistic Freezing Cellular Automata (TFCA) defined over the triangular and square grids with von Neumann neighborhoods. We say that a Cellular Automaton is Freezing and Totalistic if the active cells remain unchanged, and the new value of an inactive cell depends only on the sum of its active neighbors. We classify all the Cellular Automata in the class of TFCA, grouping them in five different classes: the Trivial rules, Turing Universal rules,Algebraic rules, Topological rules and Fractal Growing rules. At the same time, we study in this family the Stability problem, consisting in deciding whether an inactive cell becomes active, given an initial configuration.We exploit the properties of the automata in each group to show that:
- For Algebraic and Topological Rules the Stability problem is in $\text{NC}$.
- For Turing Universal rules the Stability problem is $\text{P}$-Complete.
2 citations
Cites methods from "An introduction to parallel algorit..."
...a shortest path from vertex vito vertex vj. The following proposition states that there is a fast-parallel algorithms computing an All Pairs Shortest Path matrix of an input graph G. Proposition 2.6 ([10]). There is an algorithm that computes all Pairs Shortest Paths matrix of a graph with nvertices in time O(log2 n) with O(n3 logn) processors. 3 Triangular Grid We will start our study over the regula...
[...]
...be checked in time O(log2 N) using O(N2) processors according the algorithm of Theorem 3.1. Step 4 can be done in time O(log2 N) using O(N2) processors using a connected components algorithm given in [10]. Step 5 an be done in time O(log2 N) using O(N3=logN) processors using a bi-connected components algorithm given in [10]. Step 10 can be solved in time O(logN) using O(N) processors using a vertex le...
[...]
....2 Connected components The following propositions state that the connected, bi-connected and tri-connected components of an input graph Gcan be computed by fast-parallel algorithms. Proposition 2.2 ([10]). There is an algorithm that computes the connected components of a graph with nvertices in time O(log2 n) with O(n2) processors. Proposition 2.3 ([11]). There is an algorithm that computes the bi-co...
[...]
... the distance (number of edges) between vand the root r. The following proposition shows that there is a fast-parallel algorithm that computes the level of every vertex of the graph. Proposition 2.5 ([10]). There is an algorithm that computes, on an input rooted tree (T;r) the level(v) of every vertex v2V(T) in time O(logn) and using O(n) processors, where nis the size of T. 2.2.4 All pairs shortest p...
[...]
...ive some NC algoirhtms that we will use as subroutines of our fast-parallel algorithm solving Stability. 2.2.1 Prex-sum First, we will study a general way to compute in NC called prex sum algorithm [10]. Given an associative binary operation dened on a group G, and an array A= (a1;:::;an) of nelements of G, the prex sum of Ais the vector Bof dimension nsuch that Bi= a1 ai. Computing the prex sum ...
[...]
References
More filters
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....
[...]
...Every location in the array represents a node of the tree: T [1] is the root, with children at T [2] and T [3]....
[...]
...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)....
[...]
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])....
[...]
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]....
[...]
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]....
[...]
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....
[...]