Journal Article10.1145/321992.321995
A Level Algorithm for Preemptive Scheduling
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TL;DR: A level algorithm is given that constructs optimal preemptive schedules on identical processors when the task system is a tree or when there are only two processors available, and an upper bound on its performance is derived in terms of the speeds of the processors.
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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.
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Citations
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References
Optimal scheduling for two-processor systems
Edward G. Coffman,Ron Graham +1 more
TL;DR: It is proved that the algorithm gives optimal solutions and its application to preemptive scheduling disciplines is discussed.
623
Preemptive Scheduling of Real-Time Tasks on Multiprocessor Systems
TL;DR: The authors solve the problem of scheduling a set of tasks whose operational precedence structure is representable as an acyclic directed graph and proof of an efficient algori thm for finding the minimal-length preemptive schedule for tree-structured computations.
181
Worst Case Analysis of Two Scheduling Algorithms
Shui Lam,Ravi Sethi +1 more
TL;DR: It is shown that the ratio of the lengths of their algorithm and an optimal schedule is bounded by $2 - 2/m$ and in both the nonpreemptive and the preemptive cases there exist task systems for which the ratio can be approached arbitrarily closely.
100
•Book
Preemptive scheduling of real-time tasks on multiprocessor systems
Richard R. Muntz,Edward G. Coffman +1 more
- 03 Jan 1989
TL;DR: In this paper, the problem of scheduling a set of tasks whose operational precedence structure is represented as an acyclic directed graph is addressed, assuming that preemptions are allowed.
Optimal scheduling of independent tasks on heterogeneous computing systems
Jane W. S. Liu,Ai-Tsung Yang +1 more
- 01 Jan 1974
TL;DR: Optimal scheduling algorithms which produce preemptive schedules with minimal completion times and non-preemptive schedulesWith minimal mean flow times are described, providing information concerning the relative merit of different multiprocessor systems.