Petr A. Golovach, Giannos Stamoulis, Dimitrios M. Thilikos
{"title":"Hitting Topological Minor Models in Planar Graphs is Fixed Parameter Tractable","authors":"Petr A. Golovach, Giannos Stamoulis, Dimitrios M. Thilikos","doi":"https://dl.acm.org/doi/10.1145/3583688","DOIUrl":null,"url":null,"abstract":"<p>For a finite collection of graphs ℱ, the ℱ-<span>TM-Deletion</span> problem has as input an <i>n</i>-vertex graph <i>G</i> and an integer <i>k</i> and asks whether there exists a set <i>S ⊆ V(G)</i> with <i>|S| ≤ k</i> such that <i>G \\ S</i> does not contain any of the graphs in ℱ as a topological minor. We prove that for every such ℱ, ℱ -<span>TM-Deletion</span> is fixed parameter tractable on planar graphs. Our algorithm runs in a 2<sup>𝒪(<i>k</i>2)</sup> ⋅ <i>n</i><sup>2</sup> time, or, alternatively, in 2<sup>𝒪(<i>k</i>)</sup> ⋅ <i>n</i><sup>4</sup> time. Our techniques can easily be extended to graphs that are embeddable on any fixed surface.</p>","PeriodicalId":50922,"journal":{"name":"ACM Transactions on Algorithms","volume":"7 23","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2023-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Transactions on Algorithms","FirstCategoryId":"94","ListUrlMain":"https://doi.org/https://dl.acm.org/doi/10.1145/3583688","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: 0
Abstract
For a finite collection of graphs ℱ, the ℱ-TM-Deletion problem has as input an n-vertex graph G and an integer k and asks whether there exists a set S ⊆ V(G) with |S| ≤ k such that G \ S does not contain any of the graphs in ℱ as a topological minor. We prove that for every such ℱ, ℱ -TM-Deletion is fixed parameter tractable on planar graphs. Our algorithm runs in a 2𝒪(k2) ⋅ n2 time, or, alternatively, in 2𝒪(k) ⋅ n4 time. Our techniques can easily be extended to graphs that are embeddable on any fixed surface.
期刊介绍：
ACM Transactions on Algorithms welcomes submissions of original research of the highest quality dealing with algorithms that are inherently discrete and finite, and having mathematical content in a natural way, either in the objective or in the analysis. Most welcome are new algorithms and data structures, new and improved analyses, and complexity results. Specific areas of computation covered by the journal include
combinatorial searches and objects;
counting;
discrete optimization and approximation;
randomization and quantum computation;
parallel and distributed computation;
algorithms for
graphs,
geometry,
arithmetic,
number theory,
strings;
on-line analysis;
cryptography;
coding;
data compression;
learning algorithms;
methods of algorithmic analysis;
discrete algorithms for application areas such as
biology,
economics,
game theory,
communication,
computer systems and architecture,
hardware design,
scientific computing
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
