SIAM Journal on Discrete Mathematics
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
A survey of design techniques for system-level dynamic power management
IEEE Transactions on Very Large Scale Integration (VLSI) Systems - Special section on low-power electronics and design
Non-approximability results for optimization problems on bounded degree instances
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Algorithmic problems in power management
ACM SIGACT News
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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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聽 $$\alpha $$ . 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.