Marcel Jackiewicz, Adam Kasperski, Paweł Zieliński
{"title":"Computational complexity of the recoverable robust shortest path problem with discrete recourse","authors":"Marcel Jackiewicz, Adam Kasperski, Paweł Zieliński","doi":"10.1016/j.dam.2025.03.004","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, the recoverable robust shortest path problem is investigated. Discrete budgeted interval uncertainty representation is used to model uncertain second-stage arc costs. The known complexity results for this problem are strengthened. Namely, it is shown that the recoverable robust shortest path problem is <span><math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mn>3</mn></mrow><mrow><mi>p</mi></mrow></msubsup></math></span>-hard for the arc exclusion and arc symmetric difference neighborhoods. Furthermore, it is also proven that the inner adversarial problem for these neighborhoods is <span><math><msubsup><mrow><mi>Π</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>p</mi></mrow></msubsup></math></span>-hard.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"370 ","pages":"Pages 103-110"},"PeriodicalIF":1.0000,"publicationDate":"2025-03-19","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/S0166218X25001283","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
In this paper, the recoverable robust shortest path problem is investigated. Discrete budgeted interval uncertainty representation is used to model uncertain second-stage arc costs. The known complexity results for this problem are strengthened. Namely, it is shown that the recoverable robust shortest path problem is -hard for the arc exclusion and arc symmetric difference neighborhoods. Furthermore, it is also proven that the inner adversarial problem for these neighborhoods is -hard.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
