An Optimal Execution Time Estimate of Static Versus Dynamic Allocation in Multiprocessor Systems
Blekinge Institute of Technology, Department of Computer Science and Business Administration1995 (English)In: SIAM journal on computing (Print), ISSN 0097-5397, E-ISSN 1095-7111, Vol. 24, no 4, 751-764 p.Article in journal (Refereed) Published
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 following maximal execution time ratio: g(n, k) $EQ max T$-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 by 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
Philadelphia, Pa.: SIAM publications , 1995. Vol. 24, no 4, 751-764 p.
Multiprocessing systems, Optimization, Resource allocation, Estimation, Parallel processing systems, Computer systems programming, Computer system recovery, Synchronization, Functions, Numerical methods, Combinatorial mathematics, Matrix algebra, Computational complexity
IdentifiersURN: urn:nbn:se:bth-10253ISI: A1995RP07000005Local ID: oai:bth.se:forskinfo1740CDD2344525C5C12568A3002CAB4EOAI: oai:DiVA.org:bth-10253DiVA: diva2:838335
See also Research Report 1992/1 from University of Karlskrona/Ronneby This article is written under the Project "Optimal Combinatorial Bounds Comparing Multiprocessor Architectures"2012-09-182000-03-152015-06-30Bibliographically approved