Abstract
We propose an alternative definition for the speedup of parallel algorithms. Let A be a sequential algorithm and B a parallel algorithm for solving the same problem. If A and/or B are randomized or if we are interested in their performance on a probability distribution of problem instances, the running times are described by random variables T A and T B. The speedup is usually defined as E[T A]/E[T B] where E is the arithmetic mean. This notion of speedup delivers just a number, i.e. much information about the distribution is lost. For example, there is no variance of the speedup. To define a measure for possible fluctuations of the speedup, a new notion of speedup is required. The basic idea is to define speedup as M(T A/T B) where the functional form of M has to be determined. Also, we argue that in many cases M(T A/T B) is more informative than E[(T A]/E[T B] for a typical user of A and B. We present a set of intuitive axioms that any speedup function M(T A/T B) must fulfill and prove that the geometric mean is the only solution. As a result, we now have a uniquely defined speedup function that will allow the user of an improved system to talk about the average performance improvement as well as about its possible variations.
Research supported by an ICSI Postdoctoral Fellowship (International Computer Science Institute, Berkeley CA).
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References
J. Aczél. The Notion of Mean Values. Norske Vid. Selsk. Forh. (Trondheim), 19:83–86, 1946.
J. Aczél. Lectures on Functional Equations and Their Applications, volume 19 of Mathematics in Science and Engineering. Academic Press, 1966.
J. Aczél and C. Alsina. On Synthesis of Judgements. Socio-Econ. Plann. Sci., 20(6):333–339, 1986.
J. Aczél and T. L. Saaty. Procedures for Synthesizing Ratio Judgements. J. Math. Psych., 27:93–102, 1983.
W. Ertel. Random Competition: A Simple, but Efficient Method for Parallelizing Inference Systems. In Parallelization in Inference Systems, pages 195–209. LNAI 590, Springer-Verlag, 1992.
P. J. Fleming and J. J. Wallace. How not to Lie with Statistics: The Correct Way to Summarize Benchmark Results. Comm. of the ACM, 29(3):218–221, 1986.
A. Goerdt and U. Kamps. On the Reasons for Average Superlinear Speedup in Parallel Backtrack Search. submitted for publication, 1993.
R. Mehrotra and E. F. Gehringer. Superlinear Speedup Through Randomized Algorithms. In International Conference on Parallel Processing, pages 291–300, 1985.
K. S. Natarajan. Expected Performance of Parallel Search. In International Conference on Parallel Processing, pages 121–125, 1989.
V. N. Rao and V. Kumar. Superlinear Speedup in Parallel Search. In Proc. of Foundations of Software Technology and Theor. Comp. Sci., New Dehli, 1988.
F. S. Roberts. Merging Relative Scores. J. Math. Analysis and Applications, 147:30–52, 1990.
E. Speckenmeyer, B. Monien, and O. Vornberger. Superlinear Speedup for Parallel Backtracking. In Supercomputing, LNCS 297, pages 985–994. Springer Verlag, 1988.
X.-H. Sun and J.L. Gustafson. Toward a Better Parallel Performance Metric. Parallel Computing 17, pages 1093–1109, 1991.
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© 1994 Springer-Verlag Berlin Heidelberg
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Ertel, W. (1994). On the definition of speedup. In: Halatsis, C., Maritsas, D., Philokyprou, G., Theodoridis, S. (eds) PARLE'94 Parallel Architectures and Languages Europe. PARLE 1994. Lecture Notes in Computer Science, vol 817. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58184-7_109
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DOI: https://doi.org/10.1007/3-540-58184-7_109
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