An Optimal Execution Time Estimate of Static versus Dynamic Allocation in Multiprocessor Systems
| Document type: | Researchreports |
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| Full text: | |
| Author(s): | Håkan Lennerstad, Lars Lundberg |
| Title: | An Optimal Execution Time Estimate of Static versus Dynamic Allocation in Multiprocessor Systems |
| Series: | Research Report |
| Year: | 1992 |
| Issue: | 1 |
| ISSN: | 1103-1581 |
| Organization: | Blekinge Institute of Technology |
| Department: | Dept. of Telecommunications and Mathematics (Institutionen för telekommunikation och matematik) Dept. of Telecommunications and Mathematics S-371 79 Karlskrona +46 455 780 00 http://www.hk-r.se/itm/index.html |
| Authors e-mail: | hakan@itm.hk-r.se, lasse@ide.hk-r.se |
| Language: | English |
| Abstract: | 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. |
| Subject: | Computer Science\Computersystems Computer Science\Distributed Computing Mathematics\Discrete Mathematics |
| Keywords: | multiprocessor, parallel computer, static allocation, dynamic allocation, extremal combinatorics |
| Note: | Also published in SIAM Journal of Computing, Vol. 24, No. 4, pp. 751-764, August 1995. |
| URN: | urn:nbn:se:bth-00014 |
