{"title":"树中加权顶点覆盖问题的参数化下界","authors":"P. Wojciechowski, K. Subramani","doi":"10.1007/s00236-025-00498-8","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we analyze the weighted partial vertex cover problem on undirected, vertex-weighted, edge-weighted trees (WPVCT). This problem has been studied in the literature from the perspectives of exact and approximation algorithms. We investigate this problem from the perspectives of parameterization and kernelization. The WPVCT problem finds applications in a number of domains including communications, logistics and data science. This problem is defined by a number of parameters (input, output and structural). We focus on the number of vertices in the optimal cover as the parameter of interest (output parameter). One of our results is a lower bound for parameterized algorithms for the WPVCT problem. A second result is a lower bound on the number of bits in a kernel for the same problem. Both these results are based on the Exponential Time Hypothesis (ETH).</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"62 3","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Parameterized lower bounds for the weighted vertex cover problem in trees\",\"authors\":\"P. Wojciechowski, K. Subramani\",\"doi\":\"10.1007/s00236-025-00498-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we analyze the weighted partial vertex cover problem on undirected, vertex-weighted, edge-weighted trees (WPVCT). This problem has been studied in the literature from the perspectives of exact and approximation algorithms. We investigate this problem from the perspectives of parameterization and kernelization. The WPVCT problem finds applications in a number of domains including communications, logistics and data science. This problem is defined by a number of parameters (input, output and structural). We focus on the number of vertices in the optimal cover as the parameter of interest (output parameter). One of our results is a lower bound for parameterized algorithms for the WPVCT problem. A second result is a lower bound on the number of bits in a kernel for the same problem. Both these results are based on the Exponential Time Hypothesis (ETH).</p></div>\",\"PeriodicalId\":7189,\"journal\":{\"name\":\"Acta Informatica\",\"volume\":\"62 3\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2025-08-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Informatica\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00236-025-00498-8\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, INFORMATION SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Informatica","FirstCategoryId":"94","ListUrlMain":"https://link.springer.com/article/10.1007/s00236-025-00498-8","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
Parameterized lower bounds for the weighted vertex cover problem in trees
In this paper, we analyze the weighted partial vertex cover problem on undirected, vertex-weighted, edge-weighted trees (WPVCT). This problem has been studied in the literature from the perspectives of exact and approximation algorithms. We investigate this problem from the perspectives of parameterization and kernelization. The WPVCT problem finds applications in a number of domains including communications, logistics and data science. This problem is defined by a number of parameters (input, output and structural). We focus on the number of vertices in the optimal cover as the parameter of interest (output parameter). One of our results is a lower bound for parameterized algorithms for the WPVCT problem. A second result is a lower bound on the number of bits in a kernel for the same problem. Both these results are based on the Exponential Time Hypothesis (ETH).
期刊介绍：
Acta Informatica provides international dissemination of articles on formal methods for the design and analysis of programs, computing systems and information structures, as well as related fields of Theoretical Computer Science such as Automata Theory, Logic in Computer Science, and Algorithmics.
Topics of interest include:
• semantics of programming languages
• models and modeling languages for concurrent, distributed, reactive and mobile systems
• models and modeling languages for timed, hybrid and probabilistic systems
• specification, program analysis and verification
• model checking and theorem proving
• modal, temporal, first- and higher-order logics, and their variants
• constraint logic, SAT/SMT-solving techniques
• theoretical aspects of databases, semi-structured data and finite model theory
• theoretical aspects of artificial intelligence, knowledge representation, description logic
• automata theory, formal languages, term and graph rewriting
• game-based models, synthesis
• type theory, typed calculi
• algebraic, coalgebraic and categorical methods
• formal aspects of performance, dependability and reliability analysis
• foundations of information and network security
• parallel, distributed and randomized algorithms
• design and analysis of algorithms
• foundations of network and communication protocols.
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