{"title":"Pareto-scheduling of two competing agents with total weighted tardiness being one criterion","authors":"Jinwen Sun , Rubing Chen , Qiulan Zhao","doi":"10.1016/j.dam.2025.03.026","DOIUrl":null,"url":null,"abstract":"<div><div>We study the Pareto-scheduling of two competing agents on a single machine, in which the jobs of at least one agent have their own equal processing times. When the criterion of one agent is the total weighted tardiness and the criterion of the other agent is the total completion time, the total tardiness or the total weighted completion time, the exact complexities of these problems remain open as posed by Chen et al. (2022). In this paper, we design a unified algorithm for solving these problems. As consequences, we show that these problems are solvable either in polynomial time or in pseudo-polynomial time. Combining the known results in the literature, we determine the complexity classification of nine problems.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"369 ","pages":"Pages 137-148"},"PeriodicalIF":1.0000,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166218X25001453","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We study the Pareto-scheduling of two competing agents on a single machine, in which the jobs of at least one agent have their own equal processing times. When the criterion of one agent is the total weighted tardiness and the criterion of the other agent is the total completion time, the total tardiness or the total weighted completion time, the exact complexities of these problems remain open as posed by Chen et al. (2022). In this paper, we design a unified algorithm for solving these problems. As consequences, we show that these problems are solvable either in polynomial time or in pseudo-polynomial time. Combining the known results in the literature, we determine the complexity classification of nine problems.
研究了单机上两个竞争代理的pareto调度问题，其中至少有一个代理的作业具有相等的处理时间。当一个智能体的标准是总加权延迟，另一个智能体的标准是总完工时间、总延迟时间或总加权完成时间时，这些问题的确切复杂性如Chen et al.（2022）所提出的仍然是开放的。在本文中，我们设计了一个统一的算法来解决这些问题。结果表明，这些问题在多项式时间或伪多项式时间内都是可解的。结合文献中已知的结果，我们确定了9个问题的复杂度分类。
期刊介绍：
The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal.
Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.
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