Matrix algorithms on a hypercube I: Matrix multiplication

Fox, Geoffrey; Otto, Steve W.; Hey, A J G

doi:10.1016/0167-8191(87)90060-3

Cited by 187 publications

(77 citation statements)

References 2 publications

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“…This can be done by the same approach for the general parallel matrix multiplication methods known as Fox algorithm [13] and SUMMA [21] but with extra tasks.…”

Section: Parallel Gtm Interpolationmentioning

confidence: 99%

Dimension reduction and visualization of large high-dimensional data via interpolation

Bae

Choi

Qiu

et al. 2010

Proceedings of the 19th ACM International Symposium on High Performance Distributed Computing

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The recent explosion of publicly available biology gene sequences and chemical compounds offers an unprecedented opportunity for data mining. To make data analysis feasible for such vast volume and high-dimensional scientific data, we apply high performance dimension reduction algorithms. It facilitates the investigation of unknown structures in a three dimensional visualization. Among the known dimension reduction algorithms, we utilize the multidimensional scaling and generative topographic mapping algorithms to configure the given high-dimensional data into the target dimension. However, both algorithms require large physical memory as well as computational resources. Thus, the authors propose an interpolated approach to utilizing the mapping of only a subset of the given data. This approach effectively reduces computational complexity. With minor trade-off of approximation, interpolation method makes it possible to process millions of data points with modest amounts of computation and memory requirement. Since huge amount of data are dealt, we represent how to parallelize proposed interpolation algorithms, as well. For the evaluation of the interpolated MDS by STRESS criteria, it is necessary to compute symmetric all pairwise computation with only subset of required data per process, so we also propose a simple but efficient parallel mechanism for the symmetric all pairwise computation when only a subset of data is available to each process. Our experimental results illustrate that the quality of interpolated mapping results are comparable to the mapping Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. HPDC '10 Chicago, Illinois USA Copyright 2010 ACM X-XXXXX-XX-X/XX/XX ...$10.00. results of original algorithm only. In parallel performance aspect, those interpolation methods are well parallelized with high efficiency. With the proposed interpolation method, we construct a configuration of two-million out-of-sample data into the target dimension, and the number of out-of-sample data can be increased further.

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“…This can be done by the same approach for the general parallel matrix multiplication methods known as Fox algorithm [13] and SUMMA [21] but with extra tasks.…”

Section: Parallel Gtm Interpolationmentioning

confidence: 99%

Dimension reduction and visualization of large high-dimensional data via interpolation

Bae

Choi

Qiu

et al. 2010

Proceedings of the 19th ACM International Symposium on High Performance Distributed Computing

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“…Fox [10], and Cannon [4], algorithms have been proposed for parallelizing matrix multiplication to enhance its efficiency. These approaches balance inter-process communication, dependencies, and parallelism level to maximize efficiency.…”

Section: Related Workmentioning

confidence: 99%

Parallel Hill Cipher Encryption Algorithm

Haj¹,

Qatawneh²

2018

IJCA

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Cryptography is the discipline of encoding and decoding messages. Cryptography is used frequently in people's daily lives to keep sensitive information, such as credit card information, safe. Many everyday activities can be easily monitored by unintended third parties via Internet. Hill cipher is a classic cryptography based on linear algebra that is simply a linear transformation represented by a matrix. The encoding and decoding process in Hill cipher involves matrix multiplication, which is potentially time consuming, making it one of the most well-studied problems in this field. In this paper, we implement the message passing interface (MPI) and MapReduce methods to demonstrate their effectiveness in expediting Hill cipher algorithm in parallel algorithms on a multi-core system. Simulation results show that the efficiency rates of MPI and MapReduce are 93.71 % and 53.43 respectively, with a multi-core processor on the large file size, indicating better performances compared with sequential methods.

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“…For example, a matrix multiplication application that implements Fox's Algorithm (Fox and Hey, 1987) and Cannon's Algorithm (Johnsson, Harris et al 1989) assumes parallel processes to be in a rectangular grid.…”

Section: Iterative Mapreduce -Kmeans Clustering and Matrix Multiplicamentioning

confidence: 99%

High-Performance Parallel Computing with Cloud and Cloud Technologies

Ekanayake¹,

Qiu²,

Gunarathne³

et al. 2010

Cloud Computing and Software Services

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We present our experiences in applying, developing, and evaluating cloud and cloud technologies. First, we present our experience in applying Hadoop and DryadLINQ to a series of data/compute intensive applications and then compare them with a novel MapReduce runtime developed by us, named CGL-MapReduce, and MPI. Preliminary applications are developed for particle physics, bioinformatics, clustering, and matrix multiplication. We identify the basic execution units of the MapReduce programming model and categorize the runtimes according to their characteristics. MPI versions of the applications are used where the contrast in performance needs to be highlighted. We discuss the application structure and their mapping to parallel architectures of different types, and look at the performance of these applications. Next, we present a performance analysis of MPI parallel applications on virtualized resources.

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Matrix algorithms on a hypercube I: Matrix multiplication

Cited by 187 publications

References 2 publications

Dimension reduction and visualization of large high-dimensional data via interpolation

Dimension reduction and visualization of large high-dimensional data via interpolation

Parallel Hill Cipher Encryption Algorithm

High-Performance Parallel Computing with Cloud and Cloud Technologies

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