2 research outputs found
An Optimal Execution Time Estimate of Static versus Dynamic Allocation in Multiprocessor Systems
Consider a multiprocessor with identical processors,
executing parallel programs consisting of processes.
Let and denote the execution times for the program
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
,
where the maximum is taken over all programs consisting of processes.
Any interprocess dependency structure for the programs is allowed, only
avoiding deadlock.
Overhead for synchronization and reallocation is neglected.
Basic properties of the function are established, from which we obtain
a global description of the function. Plots of 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 and , in contrast to
the np-completeness of the problems of finding optimal allocations
An Optimal Execution Time Estimate of Static Versus Dynamic Allocation in Multiprocessor Systems
Consider a multiprocessor with k identical processors, executing parallel
programs consisting of n processes. Let T/(P) and T/(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) -s-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