{"title":"A Single-Exponential Time 2-Approximation Algorithm for Treewidth","authors":"Tuukka Korhonen","doi":"10.1137/22m147551x","DOIUrl":null,"url":null,"abstract":"We give an algorithm that, given an -vertex graph and an integer , in time either outputs a tree decomposition of of width at most or determines that the treewidth of is larger than . This is the first 2-approximation algorithm for treewidth that is faster than the known exact algorithms, and in particular improves upon the previous best approximation ratio of 5 in time given by Bodlaender et al. [SIAM J. Comput., 45 (2016), pp. 317–378]. Our algorithm works by applying incremental improvement operations to a tree decomposition, using an approach inspired by a proof of Bellenbaum and Diestel [Combin. Probab. Comput., 11 (2002), pp. 541–547].","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/22m147551x","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 2
Abstract
We give an algorithm that, given an -vertex graph and an integer , in time either outputs a tree decomposition of of width at most or determines that the treewidth of is larger than . This is the first 2-approximation algorithm for treewidth that is faster than the known exact algorithms, and in particular improves upon the previous best approximation ratio of 5 in time given by Bodlaender et al. [SIAM J. Comput., 45 (2016), pp. 317–378]. Our algorithm works by applying incremental improvement operations to a tree decomposition, using an approach inspired by a proof of Bellenbaum and Diestel [Combin. Probab. Comput., 11 (2002), pp. 541–547].
期刊介绍：
The SIAM Journal on Computing aims to provide coverage of the most significant work going on in the mathematical and formal aspects of computer science and nonnumerical computing. Submissions must be clearly written and make a significant technical contribution. Topics include but are not limited to analysis and design of algorithms, algorithmic game theory, data structures, computational complexity, computational algebra, computational aspects of combinatorics and graph theory, computational biology, computational geometry, computational robotics, the mathematical aspects of programming languages, artificial intelligence, computational learning, databases, information retrieval, cryptography, networks, distributed computing, parallel algorithms, and computer architecture.
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