In this paper, we consider the homogeneous scheduling on speed-scalable processors, where the energy consumption is minimized. While most previous works have studied single-processor jobs, we focus on rigid parallel jobs, using more than one processor at the same time. Each job is specified by release date, deadline, processing volume and the number of required processors. Firstly, we develop constant-factor approximation algorithms for such interesting cases as agreeable jobs without migration and preemptive instances. Next, we propose a configuration linear program, which allows us to obtain an “almost exact” solution for the preemptive setting. Finally, in the case of non-preemptive agreeable jobs with unit-work operations, we present a three-approximation algorithm by generalization of the known exact algorithm for single-processor jobs.

中文翻译：

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并行作业节能调度的近似算法

在本文中，我们考虑了速度可扩展处理器上的同构调度，其中能耗最小。虽然以前的大部分工作都研究了单处理器作业，但我们专注于刚性并行作业，同时使用多个处理器。每个作业都由发布日期、截止日期、处理量和所需的处理器数量指定。首先，我们为诸如没有迁移和抢占式实例的令人满意的工作等有趣的情况开发了常数因子近似算法。接下来，我们提出了一个配置线性程序，它使我们能够为抢占式设置获得“几乎精确”的解决方案。最后，在具有单元工作操作的非抢占式令人满意的作业的情况下，我们通过对单处理器作业的已知精确算法的推广来提出一种三近似算法。