Online scheduling on a single machine with one restart for all jobs to minimize the weighted makespan

被引：0
|
作者：
Liang, Xiaoxiao [1 ]
Lu, Lingfa [1 ]
Sun, Xueke [1 ]
Yu, Xue [1 ]
Zuo, Lili [1 ]
机构：
[1] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China
来源：
AIMS MATHEMATICS | 2024年 / 9卷 / 01期
基金：
中国国家自然科学基金;
关键词：
scheduling; restart; the weighted makespan; online algorithm; competitive ratio; BATCH MACHINE;
D O I：
10.3934/math.2024124
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the online scheduling problem on a single machine to minimize the weighted makespan. In this problem, all jobs arrive over time and they are allowed to be restarted only once. For the general case when the processing times of all jobs are arbitrary, we show that there is no online algorithm with a competitive ratio of less than 2, which matches the lower bound of the problem without restart. That is, only one restart for all jobs is invalid for improving the competitive ratio in the general case. For the special case when all jobs have the same processing time, we present the best possible online algorithm with a competitive ratio of 1.4656, which improves the competitive ratio of 1+2 approximate to 1.618 for the problem without restart.
引用
收藏
页码：2518 / 2529
页数：12
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