The Relation of Scalability and Execution Time

نویسندگان

  • J Sherman
  • W Morrison
چکیده

\Adjustment of an inverse matrix corresponding to changes in the elements of a given column or a given row of the original matrix," Ann. 22 large systems. Isospeed scalability is a dimensionless scalar. It is easy to understand and is independent of sequential processing. When an initial speed is chosen, average speed is independent of problem size, system size, and sequential processing. In other word, it is dimensionless 19]. Therefore, scalability shows the inherited scaling characteristics of AMCs. Two AMCs are said to be computational similar if they have the same scalability over a range. Two similar algorithms, the PDD algorithm and the Reduced PDD algorithm, are carefully examed in this study. We have shown, theoretically and experimentally, that the two algorithms have the same computation and communication structure and have the same scalability. A third algorithm, the PPT algorithm is also studied to show that diierent communication structure will lead to diierent scalability, and that machine parameters may innuence the scalability considerably. Scalability and scaling similarity are very important in evaluation, benchmarking, and comparison of parallel algorithms and architectures. They have practical importance in performance debugging, compiler optimization, and selection of an optimal algorithm/machine pair for an application. Current understanding of scalability is very limited. This study is an attempt to lead to a better understanding of scalability and its practical impact. Acknowledgment The author is grateful to J. Zhu of Mississippi State University and D. Keyes of ICASE for their valuable suggestions and comments that helped improve the presentation of the paper and grateful to S. Moitra of NASA Langley Research Center in help gathering the performance data on SP2. References 1] G. Amdahl, \Validity of the single-processor approach to achieving large scale computing capabilities," in Proc. 21 and the Paragon except for communication commands. MPL is used on SP2 for message passing. The all-to-all communication is implemented by calling communication library calls, gcol is used on the Paragon and mp concat is used on the SP2. From Tables 2, 4, and 3, 5, we can see that the PPT algorithm has a smaller time increase and less average speed reduction on the SP2 than that on the Paragon. This means the PPT algorithm has a better scalability on the SP2 than on the Paragon. The better scalability may due to various reasons, principally a larger memory and a more eecient all-to-all communication subroutine available on the SP2. …

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The Relation of Scalability and Execution Time

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تاریخ انتشار 1996