{"title":"An FPT algorithm for timeline cover","authors":"Riccardo Dondi , Manuel Lafond","doi":"10.1016/j.jcss.2025.103679","DOIUrl":null,"url":null,"abstract":"<div><div>One of the most studied problem in theoretical computer science, <span>Vertex Cover</span>, has been recently considered in the temporal graph framework. Here we study a <span>Vertex Cover</span> variant, called k-<span>TimelineCover</span>. Given a temporal graph k-<span>TimelineCover</span> asks to define an interval for each vertex so that for every temporal edge existing in a timestamp <em>t</em>, at least one of the endpoints has an interval that includes <em>t</em>. The goal is to decide whether it is possible to cover every temporal edge while using vertex intervals of total span at most <em>k</em>. k-<span>TimelineCover</span> has been shown to be NP-hard, but its parameterized complexity has not been fully understood when parameterizing by the span of the solution. We settle this open problem by giving an FPT algorithm that combines two techniques, a modified form of iterative compression and a reduction to <span>Digraph Pair Cut</span>.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"154 ","pages":"Article 103679"},"PeriodicalIF":1.1000,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computer and System Sciences","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022000025000613","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
引用次数: 0
Abstract
One of the most studied problem in theoretical computer science, Vertex Cover, has been recently considered in the temporal graph framework. Here we study a Vertex Cover variant, called k-TimelineCover. Given a temporal graph k-TimelineCover asks to define an interval for each vertex so that for every temporal edge existing in a timestamp t, at least one of the endpoints has an interval that includes t. The goal is to decide whether it is possible to cover every temporal edge while using vertex intervals of total span at most k. k-TimelineCover has been shown to be NP-hard, but its parameterized complexity has not been fully understood when parameterizing by the span of the solution. We settle this open problem by giving an FPT algorithm that combines two techniques, a modified form of iterative compression and a reduction to Digraph Pair Cut.
期刊介绍:
The Journal of Computer and System Sciences publishes original research papers in computer science and related subjects in system science, with attention to the relevant mathematical theory. Applications-oriented papers may also be accepted and they are expected to contain deep analytic evaluation of the proposed solutions.
Research areas include traditional subjects such as:
• Theory of algorithms and computability
• Formal languages
• Automata theory
Contemporary subjects such as:
• Complexity theory
• Algorithmic Complexity
• Parallel & distributed computing
• Computer networks
• Neural networks
• Computational learning theory
• Database theory & practice
• Computer modeling of complex systems
• Security and Privacy.