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An Optimal Execution Time Estimate of Static versus Dynamic Allocation in Multiprocessor Systems
Responsible organisation
1992 (English)Report (Other academic)
Abstract [en]

Consider a multiprocessor with $k$ identical processors, executing parallel programs consisting of $n$ processes. Let $T_s(P)$ and $T_d(P)$ denote the execution times for the program $P$ with optimal static and dynamic allocations respectively, i. e. allocations giving minimal execution time. We derive a general and explicit formula for the maximal execution time ratio $g(n,k)=\max T_s(P)/T_d(P)$, where the maximum is taken over all programs $P$ consisting of $n$ processes. Any interprocess dependency structure for the programs $P$ is allowed, only avoiding deadlock. Overhead for synchronization and reallocation is neglected. Basic properties of the function $g(n,k)$ are established, from which we obtain a global description of the function. Plots of $g(n,k)$ are included. The results are obtained by investigating a mathematical formulation. The mathematical tools involved are essentially tools of elementary combinatorics. The formula is a combinatorial function applied on certain extremal matrices corresponding to extremal programs. It is mathematically complicated but rapidly computed for reasonable $n$ and $k$, in contrast to the np-completeness of the problems of finding optimal allocations.

Place, publisher, year, edition, pages
Blekinge Tekniska Högskola Forskningsrapport, ISSN 1103-1581 ; 1
Keyword [en]
multiprocessor, parallel computer, static allocation, dynamic allocation, extremal combinatorics
National Category
Mathematical Analysis Computer Science
URN: urn:nbn:se:bth-00014Local ID: diva2:838200
Also published in SIAM Journal of Computing, Vol. 24, No. 4, pp. 751-764, August 1995.Available from: 2012-09-18 Created: 2000-03-15 Last updated: 2015-06-30Bibliographically approved

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Lennerstad, HåkanLundberg, Lars
Mathematical AnalysisComputer Science

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