在平面图形中命中拓扑小模型是固定参数可处理的

IF 0.9 3区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

ACM Transactions on Algorithms Pub Date : 2023-05-05 DOI:https://dl.acm.org/doi/10.1145/3583688

Petr A. Golovach, Giannos Stamoulis, Dimitrios M. Thilikos

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引用次数: 0

摘要

对于一个有限图集，以一个n顶点图G和一个整数k作为输入，问是否存在一个集S V(G)，且|S|≤k，使得G \ S不包含任意一个图作为拓扑次元。证明了对于每一个这样的函数，在平面图上是固定参数可处理的。我们的算法运行时间为2个状态(k2)⋅n2，或者2个状态(k)⋅n4。我们的技术可以很容易地扩展到可嵌入在任何固定表面上的图形。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Hitting Topological Minor Models in Planar Graphs is Fixed Parameter Tractable

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 2^𝒪(k2) ⋅ n² time, or, alternatively, in 2^𝒪(k) ⋅ n⁴ time. Our techniques can easily be extended to graphs that are embeddable on any fixed surface.

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来源期刊

ACM Transactions on Algorithms COMPUTER SCIENCE, THEORY & METHODS-MATHEMATICS, APPLIED

CiteScore

3.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

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