回收时间表的能量：模型和算法
Reclaiming the energy of a schedule: models and algorithms
摘要：
我们认为一个任务图上执行的一组处理器。我们假设的映射是给定的，比如说由一个有序的任务列表在每个处理器上执行，我们的目标是优化能源消耗，同时执行规定的执行时间的约束。虽然不可能改变任务的分配，但可以改变其速度。而不是使用一个本地的方法，如ESTA，我们认为这个问题作为一个整体，并研究其复杂性的几个速度变化模型的影响。对于连续的速度，我们给出了一个封闭形式的公式，树和串并行图，我们把问题转化为一般有向无环图的几何规划问题。我们表明，经典的动态电压和频率缩放（DVFS）模型与离散模式导致一个NP完全问题，即使模式是定期分布（在实践中的一个重要的特殊情况下，我们分析的增量模型）。相反，VDD跳变模型导致多项式解。最后，我们提供了一个近似算法的增量模型，我们扩展到一般DVFS模型。
英文摘要：
We consider a task graph to be executed on a set of processors. We assume that the mapping is given, say by an ordered list of tasks to execute on each processor, and we aim at optimizing the energy consumption while enforcing a prescribed bound on the execution time. While it is not possible to change the allocation of a task, it is possible to change its speed. Rather than using a local approach such as backfilling, we consider the problem as a whole and study the impact of several speed variation models on its complexity. For continuous speeds, we give a closed-form formula for trees and series-parallel graphs, and we cast the problem into a geometric programming problem for general directed acyclic graphs. We show that the classical dynamic voltage and frequency scaling (DVFS) model with discrete modes leads to a NP-complete problem, even if the modes are regularly distributed (an important particular case in practice, which we analyze as the incremental model). On the contrary, the VDD-hopping model leads to a polynomial solution. Finally, we provide an approximation algorithm for the incremental model, which we extend for the general DVFS model.
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