Multiple quadratic forms

A case study in the design of data-parallel algorithms

Mu Cheng Wang, Wayne G. Nation, James B. Armstrong, Howard Jay Siegel, Shin-Dug Kim, Mark A. Nichols, Michael Gherrity

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Data-parallel implementations of the computationally intensive task of solving multiple quadratic forms (MQFs) have been examined. Coupled and uncoupled parallel methods are investigated, where coupling relates to the degree of interaction among the processors. Also, the impact of partitioning a large MQF problem into smaller non-interacting subtasks is studied. Trade-offs among the implementations for various data-size/machine-size ratios are categorized in terms of complex arithmetic operation counts, communication overhead, and memory storage requirements. Furthermore, the impact on performance of the mode of parallelism used is considered, specifically, SIMD versus MIMD versus SIMD/MIMD mixed-mode. From the complexity analyses, it is shown that none of the algorithms presented in this paper is best for all data-size/machine-size ratios. Thus, to achieve scalability (i.e., good performance as the number of processors available in a machine increases), instead of using a single algorithm, the approach discussed is to have a set of algorithms from which the most appropriate algorithm or combination of algorithms is selected based on the ratio calculated from the scaled machine size. The analytical results have been verified by experiments on the MasPar MP-1 (SIMD), nCUBE 2 (MIMD), and PASM (mixed-mode) prototype.

Original languageEnglish
Pages (from-to)124-139
Number of pages16
JournalJournal of Parallel and Distributed Computing
Volume21
Issue number1
DOIs
Publication statusPublished - 1994 Jan 1

Fingerprint

Parallel algorithms
Quadratic form
Parallel Algorithms
Mixed Mode
Parallel Methods
Parallel Implementation
Parallelism
Scalability
Partitioning
Count
Trade-offs
Design
Prototype
Data storage equipment
Communication
Requirements
Interaction
Experiment
Experiments

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture
  • Computer Networks and Communications
  • Artificial Intelligence

Cite this

Wang, M. C., Nation, W. G., Armstrong, J. B., Siegel, H. J., Kim, S-D., Nichols, M. A., & Gherrity, M. (1994). Multiple quadratic forms: A case study in the design of data-parallel algorithms. Journal of Parallel and Distributed Computing, 21(1), 124-139. https://doi.org/10.1006/jpdc.1994.1046
Wang, Mu Cheng ; Nation, Wayne G. ; Armstrong, James B. ; Siegel, Howard Jay ; Kim, Shin-Dug ; Nichols, Mark A. ; Gherrity, Michael. / Multiple quadratic forms : A case study in the design of data-parallel algorithms. In: Journal of Parallel and Distributed Computing. 1994 ; Vol. 21, No. 1. pp. 124-139.
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Wang, MC, Nation, WG, Armstrong, JB, Siegel, HJ, Kim, S-D, Nichols, MA & Gherrity, M 1994, 'Multiple quadratic forms: A case study in the design of data-parallel algorithms', Journal of Parallel and Distributed Computing, vol. 21, no. 1, pp. 124-139. https://doi.org/10.1006/jpdc.1994.1046

Multiple quadratic forms : A case study in the design of data-parallel algorithms. / Wang, Mu Cheng; Nation, Wayne G.; Armstrong, James B.; Siegel, Howard Jay; Kim, Shin-Dug; Nichols, Mark A.; Gherrity, Michael.

In: Journal of Parallel and Distributed Computing, Vol. 21, No. 1, 01.01.1994, p. 124-139.

Research output: Contribution to journalArticle

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