Minimizing makespan and preemption costs on a system of uniform machines

H. Shachnai, T. Tamir, Gerhard Woeginger

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

7 Citations (Scopus)
91 Downloads (Pure)


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.
Original languageEnglish
Title of host publicationProceedings of the 10th Annual European Symposium on Algorithms (ESA'2002)
EditorsR. Möhring, R. Raman
ISBN (Print)3-540-44180-8
Publication statusPublished - 2002
Event10th Annual European Symposium on Algorithms, ESA 2002 - Rome, Italy
Duration: 17 Sep 200221 Sep 2002
Conference number: 10


Conference10th Annual European Symposium on Algorithms, ESA 2002
Abbreviated titleESA


  • METIS-208659


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