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An Optimal Executio...
Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
- NATURVETENSKAP -- Data- och informationsvetenskap -- Datavetenskap (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences -- Computer Sciences (hsv//eng)
Nyckelord
- multiprocessor
- parallel computer
- static allocation
- dynamic allocation
- extremal combinatorics
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