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A tight approximation ratio of a list scheduling algorithm for a single-machine scheduling problem with a non-renewable resource
Journal of Scheduling ( IF 2 ) Pub Date : 2021-04-02 , DOI: 10.1007/s10951-021-00681-y
Susumu Hashimoto , Shinji Mizuno

In this paper, we investigate an open problem by Györgyi and Kis for a single-machine scheduling problem with a non-renewable resource (NR-SSP) and total weighted completion time criterion. The problem is NP-hard, even if every job has the same processing time, and each weight is equal to its required amount of the resource. Györgyi and Kis prove that a simple list scheduling algorithm for this special case is a 3-approximation algorithm and conjecture that the algorithm for the case is a 2-approximation algorithm. We prove their conjecture. More strongly, we show that the approximation ratio is strictly less than 2 for any instance, and for any \( \epsilon > 0 \), there exists an instance for which the approximation ratio is more than \( 2-\epsilon \).



中文翻译:

具有不可再生资源的单机调度问题的列表调度算法的严格逼近率

在本文中,我们研究了Györgyi和Kis针对具有不可再生资源(NR-SSP)和总加权完成时间准则的单机调度问题的开放问题。即使每个作业都具有相同的处理时间,并且每个权重等于其所需的资源量,问题也是NP难题。Györgyi和Kis证明了这种特殊情况的简单列表调度算法是3逼近算法,并且推测这种情况的算法是2逼近算法。我们证明他们的猜想。更有力的是,我们表明在任何情况下逼近比都严格小于2,并且对于任何\(\ epsilon> 0 \),存在一个实例,其逼近比大于\(2- \ epsilon \)

更新日期:2021-04-02
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