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A Fully Polynomial-Time Approximation Scheme for Speed Scaling with a Sleep State

机译:一种完全多项式近似方案,用于睡眠状态的速度缩放

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We study classical deadline-based preemptive scheduling of jobs in a computing environment equipped with both dynamic speed scaling and sleep state capabilities: Each job is specified by a release time, a deadline and a processing volume, and has to be scheduled on a single, speed-scalable processor that is supplied with a sleep state. In the sleep state, the processor consumes no energy, but a constant wake-up cost is required to transition back to the active state. In contrast to speed scaling alone, the addition of a sleep state makes it sometimes beneficial to accelerate the processing of jobs in order to transition the processor to the sleep state for longer amounts of time and incur further energy savings. The goal is to output a feasible schedule that minimizes the energy consumption. Since the introduction of the problem by Irani et al. (ACM Trans Algorithms 3(4), 2007), its exact computational complexity has been repeatedly posed as an open question (see e.g. Albers and Antoniadis in ACM Trans Algorithms 10(2):9, 2014; Baptiste et al. in ACM Trans Algorithms 8(3):26, 2012; Irani and Pruhs in SIGACT News 36(2):63-76, 2005). The currently best known upper and lower bounds are a 4 / 3-approximation algorithm and NP-hardness due to Albers and Antoniadis (2014) and Kumar and Shannigrahi (CoRR, 2013. ), respectively. We close the aforementioned gap between the upper and lower bound on the computational complexity of speed scaling with sleep state by presenting a fully polynomial-time approximation scheme for the problem. The scheme is based on a transformation to a non-preemptive variant of the problem, and a discretization that exploits a carefully defined lexicographical ordering among schedules.
机译:我们研究了配备动态缩放和睡眠状态功能的计算环境中的经典截止日期初始调度:每个作业由释放时间,截止日期和处理卷指定,并且必须在单个上计划,速度可伸缩的处理器,提供睡眠状态。在睡眠状态下,处理器不消耗能量,但是需要持续唤醒成本来转换回活动状态。与单独的速度缩放相比,添加睡眠状态使得有时有利于加速作业的处理,以便将处理器转换为睡眠状态以实现更长的时间并产生进一步节能。目标是输出可行的时间表,可最大限度地减少能量消耗。自Irani等人引入问题以来。 (ACM Trans算法3(4),2007),其确切的计算复杂性一再作为打开问题(参见Acm Trans算法10(2):9,2014中的Albers和Antoniadis; Baptiste等人。在ACM Trans中算法8(3):2012:26,2012;伊拉尼和Pruhs在Sigact News 36(2):63-76,2005))。由于Albers和Antoniadis(2014)和Kumar和Shannigrahi(Corl,2013),目前最着名的上限和下限是一种4/3近似算法和NP硬度,分别是葡萄干和Kumar和Shannigrahi(Cor 2013.)。通过呈现问题的完全多项式时间近似方案,缩小了速度缩放计算复杂性的上述差距和下限。该方案基于对问题的非抢占变体的转换,以及利用计划之间仔细定义的词典排序的离散化。

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