Scheduling Shared Continuous Resources on Many-Cores

A. Brinkmann, P. Kling, F. Meyer auf der Heide, L. Nagel, S. Riechers, T. Süss, in: Proceedings of the 26th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 2014, pp. 128–137.

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We consider the problem of scheduling a number of jobs on $m$ identical processors sharing a continuously divisible resource. Each job j comes with a resource requirement r_j \in {0,1}. The job can be processed at full speed if granted its full resource requirement. If receiving only an x-portion of r_j, it is processed at an x-fraction of the full speed. Our goal is to find a resource assignment that minimizes the makespan (i.e., the latest completion time). Variants of such problems, relating the resource assignment of jobs to their \emph{processing speeds}, have been studied under the term discrete-continuous scheduling. Known results are either very pessimistic or heuristic in nature.In this paper, we suggest and analyze a slightly simplified model. It focuses on the assignment of shared continuous resources to the processors. The job assignment to processors and the ordering of the jobs have already been fixed. It is shown that, even for unit size jobs, finding an optimal solution is NP-hard if the number of processors is part of the input. Positive results for unit size jobs include an efficient optimal algorithm for 2 processors. Moreover, we prove that balanced schedules yield a 2-1/m-approximation for a fixed number of processors. Such schedules are computed by our GreedyBalance algorithm, for which the bound is tight.
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Proceedings of the 26th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA)
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128-137
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Brinkmann A, Kling P, Meyer auf der Heide F, Nagel L, Riechers S, Süss T. Scheduling Shared Continuous Resources on Many-Cores. In: Proceedings of the 26th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA). ; 2014:128-137. doi:10.1145/2612669.2612698
Brinkmann, A., Kling, P., Meyer auf der Heide, F., Nagel, L., Riechers, S., & Süss, T. (2014). Scheduling Shared Continuous Resources on Many-Cores. In Proceedings of the 26th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA) (pp. 128–137). https://doi.org/10.1145/2612669.2612698
@inproceedings{Brinkmann_Kling_Meyer auf der Heide_Nagel_Riechers_Süss_2014, title={Scheduling Shared Continuous Resources on Many-Cores}, DOI={10.1145/2612669.2612698}, booktitle={Proceedings of the 26th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA)}, author={Brinkmann, Andre and Kling, Peter and Meyer auf der Heide, Friedhelm and Nagel, Lars and Riechers, Sören and Süss, Tim }, year={2014}, pages={128–137} }
Brinkmann, Andre, Peter Kling, Friedhelm Meyer auf der Heide, Lars Nagel, Sören Riechers, and Tim Süss. “Scheduling Shared Continuous Resources on Many-Cores.” In Proceedings of the 26th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 128–37, 2014. https://doi.org/10.1145/2612669.2612698.
A. Brinkmann, P. Kling, F. Meyer auf der Heide, L. Nagel, S. Riechers, and T. Süss, “Scheduling Shared Continuous Resources on Many-Cores,” in Proceedings of the 26th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 2014, pp. 128–137.
Brinkmann, Andre, et al. “Scheduling Shared Continuous Resources on Many-Cores.” Proceedings of the 26th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 2014, pp. 128–37, doi:10.1145/2612669.2612698.
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