Theoretical Computer Science ( IF 1.1 ) Pub Date : 2017-09-22 , DOI: 10.1016/j.tcs.2017.09.014 Vincent Chau , Xin Chen , Ken C.K. Fong , Minming Li , Kai Wang
We study the following flow shop scheduling problem on two processors. We are given n jobs with a common deadline D, where each job j has workload on processor i and a set of processors which can vary their speed dynamically. Job j can be executed on the second processor if the execution of job j is completed on the first processor. Our objective is to find a feasible schedule such that all jobs are completed by the common deadline D with minimized energy consumption. For this model, we present a linear program for the discrete speed case, where the processor can only run at specific speeds in and the job execution order is fixed. We also provide a -approximation algorithm for the arbitrary order case and for continuous speed model where m is the number of processors and α is a parameter of the processor.
We then introduce a new variant of flow shop scheduling problem called sense-and-aggregate model motivated by data aggregation in wireless sensor networks where the base station needs to receive data from sensors and then compute a single aggregate result. In this model, the first processor will receive unit size data from sensors and the second processor is responsible for calculating the aggregate result. The second processor can decide when to aggregate and the workload that needs to be done to aggregate x data will be and another unit size data will be generated as the result of the partial aggregation which will then be used in the next round aggregation. Our objective is to find a schedule such that all data are received and aggregated by the deadline with minimum energy consumption. We present an dynamic programming algorithm when and a greedy algorithm when .
Finally, we investigate the performance of the flowshop problem when the order of jobs is fixed by comparing it to the approximation algorithm with an arbitrary order. We show experimentally that the approximation ratio is close to 1 when there are few machines and when there are more jobs.
中文翻译:
用于动态电压调节的双CPU的Flow Shop
我们在两个处理器上研究以下流水车间调度问题。我们给n个工作有共同的截止日期D,其中每个工作j都有工作量在处理器i和一组可以动态改变速度的处理器上。作业Ĵ可以在第二处理器上,如果作业的执行来执行Ĵ在第一处理器上完成。我们的目标是找到一个可行的时间表,使所有工作在共同的截止日期D之前完成,同时将能耗降至最低。对于此模型,我们为离散速度情况提供了一个线性程序,其中处理器只能以特定速度运行。并且作业执行顺序是固定的。我们还提供-用于任意阶数情况和连续速度模型的近似算法,其中m是处理器数量,α是处理器参数。
然后,我们介绍了一种新的流水车间调度问题变体,称为感知和聚合模型,该模型由无线传感器网络中的数据聚合驱动,基站需要从传感器接收数据,然后计算单个聚合结果。在此模型中,第一处理器将从传感器接收单元尺寸数据,第二处理器负责计算合计结果。第二个处理器可以决定何时聚合以及聚合x数据所需完成的工作量部分聚合的结果将生成另一个单位尺寸的数据,然后将在下一轮聚合中使用该数据。我们的目标是找到一个时间表,以便在截止日期之前以最低的能耗接收和汇总所有数据。我们提出一个 动态规划算法何时 和一个贪婪算法,当 。
最后,通过将作业的顺序与任意顺序的近似算法进行比较,我们研究了流程顺序固定时flowshop问题的性能。我们通过实验表明,当机器少,工作多时,近似率接近1。