Greed Works-Online Algorithms for Unrelated Machine Stochastic Scheduling

• 成果类型: Article
• 署名作者: Gupta, Varun; Moseley, Benjamin; Uetz, Marc; Xie, Qiaomin
• 署名单位: University of Chicago; Carnegie Mellon University; University of Twente; Massachusetts Institute of Technology (MIT)
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2019.0999
• 发表日期: 2020
• 页码: 497-516
• 关键词: exponential service times; completion-time; flow time; minimize; approximation; tasks

摘要

This paper establishes performance guarantees for online algorithms that schedule stochastic, nonpreemptive jobs on unrelated machines to minimize the expected total weighted completion time. Prior work on unrelated machine scheduling with stochastic jobs was restricted to the offline case and required linear or convex programming relaxations for the assignment of jobs to machines. The algorithms introduced in this paper are purely combinatorial. The performance bounds are of the same order of magnitude as those of earlier work and depend linearly on an upper bound on the squared coefficient of variation of the jobs' processing times. Specifically for deterministic processing times, without and with release times, the competitive ratios are 4 and 6, respectively. As to the technical contribution, this paper shows how dual fitting techniques can be used for stochastic and nonpreemptive scheduling problems.