{"title":"Computation of lower tolerances of combinatorial bottleneck problems","authors":"Gerold Jäger , Marcel Turkensteen","doi":"10.1016/j.disopt.2025.100887","DOIUrl":null,"url":null,"abstract":"<div><div>This paper considers the computation of lower tolerances of combinatorial optimization problems with an objective of type bottleneck, in which the objective is to minimize the element with maximum cost of a feasible solution. A lower tolerance can be defined as the supremum decrease such that the objective value remains the same. We develop a computational approach for generic problems with objective of type bottleneck and two specific approaches for the Linear Bottleneck Assignment Problem and the Bottleneck Shortest Path Problem, which have a similar complexity as solution approaches for these two problems. Finally, we present some experimental results on random instances for these problems.</div></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"56 ","pages":"Article 100887"},"PeriodicalIF":0.9000,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Optimization","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1572528625000106","RegionNum":4,"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
This paper considers the computation of lower tolerances of combinatorial optimization problems with an objective of type bottleneck, in which the objective is to minimize the element with maximum cost of a feasible solution. A lower tolerance can be defined as the supremum decrease such that the objective value remains the same. We develop a computational approach for generic problems with objective of type bottleneck and two specific approaches for the Linear Bottleneck Assignment Problem and the Bottleneck Shortest Path Problem, which have a similar complexity as solution approaches for these two problems. Finally, we present some experimental results on random instances for these problems.
期刊介绍:
Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.