A CORRECTNESS PROOF OF PARALLEL SCAN

1994 ◽  
Vol 04 (03) ◽  
pp. 329-338 ◽  
Author(s):  
JOHN T. O’DONNELL
Keyword(s):  
Parallel Programming ◽  
Formal Specification ◽  
Parallel Architecture ◽  
Divide And Conquer ◽  
Functional Language ◽  
Correctness Proof ◽  
Equational Reasoning ◽  
Parallel Scan

The parallel scan algorithm plays an important role in parallel programming, but previous explanations of it generally rely on informal methods that fail to establish its correctness. Equational reasoning in a pure functional language provides a formal vehicle for stating the parallel scan algorithm and proving that a parallel architecture executes it correctly. The two key ideas in the proof are (1) a collection of lemmas that show how folds and scans can be decomposed into smaller problems, supporting a divide-and-conquer strategy, and (2) a formal specification of the abstract parallel architecture in the same language used to specify the problem, making it possible to reason formally about how the architecture executes the algorithm.

$\mathcal{HDC}$: A HIGHER-ORDER LANGUAGE FOR DIVIDE-AND-CONQUER

2000 ◽  
Vol 10 (02n03) ◽  
pp. 239-250 ◽  
Author(s):  
CHRISTOPH A. HERRMANN ◽  
CHRISTIAN LENGAUER
Keyword(s):  
Parallel Programming ◽  
Parallel Implementation ◽  
Higher Order ◽  
Divide And Conquer ◽  
Functional Language ◽  
Polynomial Multiplication ◽  
Functional Program ◽  
Design Decisions ◽  
Order Language

We propose the higher-order functional style for the parallel programming of algorithms. The functional language [Formula: see text], a subset of the language Haskell, facilitates the clean integration of skeletons into a functional program. Skeletons are predefined programming schemata with an efficient parallel implementation. We report on our compiler, which translates [Formula: see text] programs into C+MPI, especially on the design decisions we made. Two small examples, the n queens problem and Karatsuba's polynomial multiplication, are presented to demonstrate the programming comfort and the speedup one can obtain.

A functional language to implement the divide-and-conquer Delaunay triangulation algorithm

2005 ◽  
Vol 168 (1) ◽  
pp. 178-191 ◽  
Author(s):  
André L. Moura ◽  
José R. Camacho ◽  
Sebastião C. Guimarães ◽  
Carlos H. Salerno
Keyword(s):  
Delaunay Triangulation ◽  
Divide And Conquer ◽  
Functional Language

scholarly journals Investigating Parallel Programming Paradigms in HeMPS MPSoC Platform

2019 ◽  
Author(s):  
Geaninne Lopes ◽  
Aline Mello ◽  
Ewerson Carvalho ◽  
César Marcon
Keyword(s):  
Parallel Programming ◽  
Power Dissipation ◽  
Execution Time ◽  
Matrix Multiplication ◽  
Divide And Conquer ◽  
Image Manipulation ◽  
Multiprocessor System ◽  
Input Size ◽  
Programming Paradigms ◽  
The Impact

This work investigates the use of parallel programming paradigms in the development of applications targeting a Multiprocessor System-on-Chip (MPSoC). We implemented Matrix Multiplication, Image Manipulation and Advanced Encryption Standard (AES) applications in the Master-Slave, Pipeline and Divide-and-Conquer paradigms, and applied execution time and power dissipation as criteria for evaluating the performance of the applications executing according to the paradigms on an MPSoC architecture. The obtained results allowed ​us to conclude that there are optimal application-paradigm relations. Pipeline presents lower execution time and lower power dissipation for the Image Manipulation application; whereas, Master-Slave performs better for the Matrix Multiplication and AES applications. However, when the input size of the applications increases, the Divide-and-Conquer paradigm tends to minimize the execution time for Matrix Multiplication application. ​The main contributions of this work are the development of applications, considering different paradigms, and the impact evaluation of these paradigms on MPSoC architecture.

Parallel functional programming in Eden

2005 ◽  
Vol 15 (3) ◽  
pp. 431-475 ◽  
Author(s):  
RITA LOOGEN ◽  
YOLANDA ORTEGA-MALLÉN ◽  
RICARDO PEÑA-MARÍ
Keyword(s):  
Parallel Programming ◽  
Case Studies ◽  
Functional Programming ◽  
General Purpose ◽  
Functional Language ◽  
Lazy Evaluation ◽  
Comprehensive Description ◽  
Programming Methodology ◽  
And Performance ◽  
Parallel Evaluation

Eden extends the non-strict functional language Haskell with constructs to control parallel evaluation of processes. Although processes are defined explicitly, communication and synchronisation issues are handled in a way transparent to the programmer. In order to offer effective support for parallel evaluation, Eden's coordination constructs override the inherently sequential demand-driven (lazy) evaluation strategy of its computation language Haskell. Eden is a general-purpose parallel functional language suitable for developing sophisticated skeletons – which simplify parallel programming immensely – as well as for exploiting more irregular parallelism that cannot easily be captured by a predefined skeleton. The paper gives a comprehensive description of Eden, its semantics, its skeleton-based programming methodology – which is applied in three case studies – its implementation and performance. Furthermore it points at many additional results that have been achieved in the context of the Eden project.

CALCULATING AN OPTIMAL HOMOMORPHIC ALGORITHM FOR BRACKET MATCHING

1999 ◽  
Vol 09 (03) ◽  
pp. 335-345 ◽  
Author(s):  
ZHENJIANG HU ◽  
MASATO TAKEICHI
Keyword(s):  
Parallel Programming ◽  
Parallel Algorithm ◽  
Parallel Computation ◽  
Divide And Conquer ◽  
Recognition Problem ◽  
Language Recognition ◽  
Formal Derivation ◽  
Parallel Software ◽  
Simple Language ◽  
Compilation Techniques

It is widely recognized that a key problem of parallel computation is in the development of both efficient and correct parallel software. Although many advanced language features and compilation techniques have been proposed to alleviate the complexity of parallel programming, much effort is still required to develop parallelism in a formal and systematic way. In this paper, we intend to clarify this point by demonstrating a formal derivation of a correct but efficient homomorphic parallel algorithm for a simple language recognition problem known as bracket matching. To the best of our knowledge, our formal derivation leads to a novel divide-and-conquer parallel algorithm for bracket matching.

Research and Application of Parallel Computing under Linux

2013 ◽  
Vol 756-759 ◽  
pp. 2825-2828
Author(s):  
Xue Chun Wang ◽  
Quan Lu Zheng
Keyword(s):  
Parallel Computing ◽  
Parallel Processing ◽  
High Performance Computing ◽  
Parallel Programming ◽  
High Performance ◽  
Performance Testing ◽  
Divide And Conquer ◽  
Parallel Computer ◽  
Super Computing ◽  
Performance Computing

Parallel computing is in parallel computer system for parallel processing of data and information, often also known as the high performance computing or super computing. The content of parallel computing were introduced, the realization of parallel computing and MPI parallel programming under Linux environment were described. The parallel algorithm based on divide and conquer method to solve rectangle placemen problem was designed and implemented with two processors. Finally, Through the performance testing and comparison, we verified the efficiency of parallel computing.

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