Abstract
This paper considers scheduling tasks while minimizing the power consumption of one or more processors, each of which can go to sleep at a fixed cost \(\alpha \). There are two natural versions of this problem, both considered extensively in recent work: minimize the total power consumption (including computation time), or minimize the number of “gaps” in execution. For both versions in a multiprocessor system, we develop a polynomial-time algorithm based on sophisticated dynamic programming. In a generalization of the power-saving problem, where each task can execute in any of a specified set of time intervals, we develop a \((1+{2 \over 3} \alpha )\)-approximation, and show that dependence on \(\alpha \) is necessary. In contrast, the analogous multi-interval gap scheduling problem is set-cover hard (and thus not \(o(\lg n)\)-approximable), even in the special cases of just two intervals per job or just three unit intervals per job. We also prove several other hardness-of-approximation results. Finally, we give an \(O(\sqrt{n})\)-approximation for maximizing throughput given a hard upper bound on the number of gaps.
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Acknowledgments
M. Ghodsi—Supported in part by Institute for Theoretical Physics and Mathematics (IPM) under Grant Numbers CS1385-2-01 and CS1384-6-01. We thank the anonymous referees for helpful comments.
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A preliminary version of this paper appeared in Proceedings of the 19th ACM Symposium on Parallelism in Algorithms and Architectures, 2007, pp. 46–54.
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Demaine, E.D., Ghodsi, M., Hajiaghayi, M. et al. Scheduling to minimize gaps and power consumption. J Sched 16, 151–160 (2013). https://doi.org/10.1007/s10951-012-0309-6
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DOI: https://doi.org/10.1007/s10951-012-0309-6