Scheduling to minimize gaps and power consumption

Authors:
Erik D. Demaine;Mohammad Ghodsi;Mohammad Taghi Hajiaghayi;Amin S. Sayedi-Roshkhar;Morteza Zadimoghaddam
Affiliations:
M.I.T., Cambridge, MA;Sharif University of Technology, Tehran, Iran;M.I.T., Cambridge, MA;Sharif University of Technology, Tehran, Iran;Sharif University of Technology, Tehran, Iran
Venue:
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Year:
2007

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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 α. 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 + 23 α)-approximation, and show that dependence on α 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(√n)-approximation for maximizing throughput given a hard upper bound on the number of gaps.