- Author:
- Gilbert H. Young,
- Supervisor:
- Joseph Y-T. Leung
The theory of deterministic scheduling has expanded rapidly during the last three decades. Today, the remaining open problems in classical scheduling theory are still being attacked heavily. In this dissertation we consider the complexity of several classical scheduling problems.
The complexity of the following scheduling problem about makespan has been open for many years: nonpreemptively schedule tasks with chain precedence constraint on m $>$ 1 identical processors so as to minimize the makespan. We show that the problem is strongly NP-hard for any fixed m $>$ 1.
The complexity of the following scheduling problems about mean flow time and mean weighted flow time has been open for many years: (1) nonpreemptively schedule tasks with chain precedence constraint on m $>$ 1 identical processors so as to minimize the mean flow time, (2) preemptively schedule tasks with chain precedence constraint on m $>$ 1 identical processors so as to minimize the mean flow time, (3) preemptively schedule equal-execution-time tasks with release time and weight on m $>$ 1 identical processors so as to minimize the mean weighted flow time, and (4) preemptively schedule tasks with release time on m $>$ 1 identical processors so as to minimize the mean flow time. We show that (1) is strongly NP-hard for any fixed m $>$ 1. By showing that preemption cannot reduce the mean weighted flow time with chain precedence constraint, it follows that (2) is also strongly NP-hard for any fixed m $>$ 1. We also show that (3) is NP-hard for arbitrary m and (4) is NP-hard for any fixed m $>$ 1.
The complexity of the following scheduling problem about makespan and mean flow time has been open for many years: preemptively schedule tasks on m $>$ 1 processors with the objective of minimizing the makespan subject to the constraint that it must have the minimum mean flow time. We give an O(nlogn) time algorithm to find an optimal schedule. Our algorithm generates schedules with at most m $-$ 1 preemptions. We also show that an optimal nonpreemptive schedule can be almost twice as long as an optimal preemptive schedule. Our results suggest that preemption is extremely beneficial in minimizing the makespan and mean flow time simultaneously.
The complexity of the following scheduling problem about total tardiness has been open for many years: nonpreemptively schedule equal-execution-time tasks with chain precedence constraint on one processor so as to minimize the total tardiness. We show that the problem is strongly NP-hard.
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