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
01 Jan 2005
TL;DR: In this paper, the authors studied the complexity of self-assembly, fault-tolerant selfassembly, DNA robotics devices, and DNA computing devices in the context of DNA tiling lattices.
Abstract: The construction of complex systems at the 1–100 nanometer (1 nanometer = 10 −9 meter) scale is a key challenge in current nanoscience. This challenge can be most effectively addressed by the “bottom-up” nano-construction methodology based on self-assembly, a process in which substructures autonomously associate with each other to form superstructures driven by the selective affinity of the substructures. DNA, with its immense information encoding capacity and well defined Watson-Crick complementarity, has recently emerged as an excellent material for constructing self-assembled nano-structures. In this dissertation, we study four closely related aspects of DNA based self-assembly and nano-devices: complexity of self-assembly, fault-tolerant self-assembly, DNA robotics devices, and DNA computing devices.
Complexity of self-assembly. We establish a framework that models assemblies resulting from the cooperative effects of repulsion and attraction forces in a general setting of graphs. By capturing a much wider range of interesting self-assembly phenomena, it advances previous work that models simple rectangular grid structures formed by only attraction force. We define an accretive graph assembly model and a self-destructible graph assembly model, and obtain several complexity results including the first PSPACE-complete result in the study of self-assembly.
Fault tolerant self-assembly. Fault tolerance is essential for building complex synthetic self-assembled systems at the molecular scale. In the practical context of algorithmic DNA tiling lattices, we propose an information encoding scheme using overlaid redundant computation, which, for the first time, reduces the error rate from e to e3 without increasing the size of the assembled lattice.
DNA robotics devices. A major challenge in nanotechnology is to precisely transport a nanoscale object from one location on a nano-structure to another location along a designated path. To address this challenge, we design DNA motors capable of autonomous, unidirectional, progressive linear motion along self-assembled DNA tracks. The practicality of the designs is partially supported by the experimental construction of a three-anchorage autonomous DNA walking device.
DNA computing devices. Building on the designs of the above robotics devices, we obtain the designs of autonomous DNA mechanical computing devices embedded in DNA lattices. These devices represent a novel converging point for studies on nano-lattice assembly, nano-robotics, and nano-computing. In particular, we present the designs of an autonomous universal DNA Turing machine and an autonomous universal DNA cellular automaton.
2 citations
Cites background from "An introduction to parallel algorit..."
...Cellular automata thus also represent a category of more compact universal computing devices [32, 38]....
[...]
11 Sep 2008
TL;DR: This paper presents the parallelism facets in the numerical simulation of the distributed-parameter systems using the finite element method and describes some computational aspects for parallel computers in computer-aided design of the electromagnetic devices using the infinite element method.
Abstract: In this paper we present the parallelism facets in the numerical simulation of the distributed-parameter systems using the finite element method. As a parallel implementation of the finite element (FE) programs, the domain decomposition method is the best among three possible decomposition strategies for the parallel solution of partial derivative equations (PDE), namely, operator decomposition, function-space decomposition and domain decomposition. This is one of the motivations to present the inherent parallelism in finite element programs.
The principal objective of the paper is to describe some computational aspects for parallel computers in computer-aided design of the electromagnetic devices using the finite element method. For each stage of FE program there is an inherent parallelism of the algorithm that can be exploited on the new architectures.
2 citations
Cites background or methods from "An introduction to parallel algorit..."
...In many engineering problems we identify an obvious parallelism so that the use the new architectures is a natural approach [10]....
[...]
...For the advanced architectures, new algorithms must be developed and the domain decomposition techniques are powerful iterative methods that are promising for parallel computation ([9], [10], [15])....
[...]
TL;DR: The fast Fourier transform completes the connection given by Draux between the three-term recurrence relationship and the Euclidian algorithm and presents an algorithm for computing orthogonal polynomials.
2 citations
TL;DR: Deterministic and randomized multisearch algorithms that are very communication efficient are described that are developed for abstract parallel models like the PRAM.
Abstract: Searching is one of the most important algorithmic problems, used as a subroutine in many applications Accordingly, designing search algorithms is in the center of research on data structures since decades In this paper we aim to survey recent developments in designing parallel search algorithms where parallel machines are used to answer many search queries in parallel, so called multisearch algorithms We briefly describe the current state of multisearch algorithms based on hashing and binary search, as they are developed for abstract parallel models like the PRAM The main part of the paper describes deterministic and randomized multisearch algorithms that are very communication efficient As a computation and cost model we employ Valiant's BSP model and its variant BSP* due to Baumker et al
2 citations
Cites background from "An introduction to parallel algorit..."
...In [ 20 ], upper and lower bounds for this problem on the PRAM model can be found....
[...]
Posted Content•
TL;DR: In this article, the authors study the problem of deciding whether a cell is unstable or not in the context of asynchronous updating schemes and show that the problem is in NP-complete.
Abstract: In this paper we study the family of freezing cellular automata (FCA) in the context of asynchronous updating schemes. A cellular automaton is called freezing if there exists an order of its states, and the transitions are only allowed to go from a lower to a higher state. A cellular automaton is asynchronous if at each time-step only one cell is updated. Given configuration, we say that a cell is unstable if there exists a sequential updating scheme that changes its state. In this context, we define the problem AsyncUnstability, which consists in deciding if a cell is unstable or not. In general AsyncUnstability is in NP, and we study in which cases we can solve the problem by a more efficient algorithm.
We begin showing that AsyncUnstability is in NL for any one-dimensional FCA. Then we focus on the family of life-like freezing CA (LFCA), which is a family of two-dimensional two-state FCA that generalize the freezing version of the game of life, known as life without death. We study the complexity of AsyncUnstability for all LFCA in the triangular and square grids, showing that almost all of them can be solved in NC, except for one rule for which the problem is NP-complete.
2 citations
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....
[...]