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A Level Algorithm for Preemptive Scheduling

A Level Algorithm for Preemptive Scheduling Muntz and Coffman give a level algorithm that constructs optimal preemptive schedules on identical processors when the task system is a tree or when there are only two processors available. Their algorithm is adapted here to handle processors of different speeds. The new algorithm is optimal for independent tasks on any number of processors and for arbitrary task systems on two processors, but not on three or more processors, even for trees. By taking the algorithm as a heuristic on m processors and using the ratio of the lengths of the constructed and optimal schedules as a measure, an upper bound on its performance is derived in terms of the speeds of the processors. It is further shown that 1.23√ m is an upper bound over all possible processor speeds and that the 1.23√ m bound can be improved at most by a constant factor, by giving an example of a system for which the bound 0.35√ m can be approached asymptotically. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the ACM (JACM) Association for Computing Machinery

A Level Algorithm for Preemptive Scheduling

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Publisher
Association for Computing Machinery
Copyright
The ACM Portal is published by the Association for Computing Machinery. Copyright © 2010 ACM, Inc.
Subject
Sequencing and scheduling
ISSN
0004-5411
DOI
10.1145/321992.321995
Publisher site
See Article on Publisher Site

Abstract

Muntz and Coffman give a level algorithm that constructs optimal preemptive schedules on identical processors when the task system is a tree or when there are only two processors available. Their algorithm is adapted here to handle processors of different speeds. The new algorithm is optimal for independent tasks on any number of processors and for arbitrary task systems on two processors, but not on three or more processors, even for trees. By taking the algorithm as a heuristic on m processors and using the ratio of the lengths of the constructed and optimal schedules as a measure, an upper bound on its performance is derived in terms of the speeds of the processors. It is further shown that 1.23√ m is an upper bound over all possible processor speeds and that the 1.23√ m bound can be improved at most by a constant factor, by giving an example of a system for which the bound 0.35√ m can be approached asymptotically.

Journal

Journal of the ACM (JACM)Association for Computing Machinery

Published: Jan 1, 1977

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