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引用次数: 0
摘要
在本文中,我们讨论了有 m 台相同机器和 n 个作业的调度问题,其中每个作业都必须分配给某台机器。调度问题的目标是最小化作业的加权有效时间,即作业的最大加权完成时间。这个调度问题是并行机调度问题中最小化作业间隔的一般化。我们针对该问题提出了一种(\(2-\frac{1}{m}\))近似算法和一种随机高效多项式时间近似方案(EPTAS)。我们还为机器数量固定的特殊情况设计了一种随机全多项式时间近似方案(FPTAS)。
Randomized approximation schemes for minimizing the weighted makespan on identical parallel machines
In this paper, we discuss scheduling problems with m identical machines and n jobs where each job has to be assigned to some machine. The objective is to minimize the weighted makespan of jobs, i.e., the maximum weighted completion time of jobs. This scheduling problem is a generalization of minimizing the makespan on parallel machine scheduling problem. We present a (\(2-\frac{1}{m}\))-approximation algorithm and a randomized efficient polynomial time approximation scheme (EPTAS) for the problem. We also design a randomized fully polynomial time approximation scheme (FPTAS) for the special case when the number of machines is fixed.
期刊介绍:
The objective of Journal of Combinatorial Optimization is to advance and promote the theory and applications of combinatorial optimization, which is an area of research at the intersection of applied mathematics, computer science, and operations research and which overlaps with many other areas such as computation complexity, computational biology, VLSI design, communication networks, and management science. It includes complexity analysis and algorithm design for combinatorial optimization problems, numerical experiments and problem discovery with applications in science and engineering.
The Journal of Combinatorial Optimization publishes refereed papers dealing with all theoretical, computational and applied aspects of combinatorial optimization. It also publishes reviews of appropriate books and special issues of journals.