Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
Scheduling Multiprocessor Tasks to Minimize Schedule Length
IEEE Transactions on Computers
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Makespan minimization in job shops: a polynomial time approximation scheme
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Preemptive scheduling of parallel jobs on multiprocessors
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
A Level Algorithm for Preemptive Scheduling
Journal of the ACM (JACM)
Preemptive Scheduling of Uniform Processor Systems
Journal of the ACM (JACM)
A PTAS for the multiple knapsack problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximation Schemes for Scheduling on Uniformly Related and Identical Parallel Machines
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Optimal preemptive scheduling for general target functions
Journal of Computer and System Sciences
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It is well known that for preemptive scheduling on uniform machines there exist polynomial time exact algorithms, whereas for nonpreemptive scheduling there are probably no such algorithms. However, it is not clear how many preemptions (in total, or per job) suffice in order to guarantee an optimal polynomial time algorithm. In this paper we investigate exactly this hardness gap, formalized as two variants of the classic preemptive scheduling problem. In generalized multiprocessor scheduling (GMS), we have job-wise or total bound on the number of preemptions throughout a feasible schedule. We need to find a schedule that satisfies the preemption constraints, such that the maximum job completion time is minimized. In minimum preemptions scheduling (MPS), the only feasible schedules are preemptive schedules with smallest possible makespan. The goal is to find a feasible schedule that minimizes the overall number of preemptions. Both problems are NP-hard, even for two machines and zero preemptions.For GMS, we develop polynomial time approximation schemes, distinguishing between the cases where the number of machines is fixed, or given as part of the input. For MPS, we derive matching lower and upper bounds on the number of preemptions required by any optimal schedule.