排除小拓扑子图的图同构检验

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

ACM Transactions on Algorithms Pub Date : 2024-03-13 DOI:10.1145/3651986

Daniel Neuen

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引用次数: 0

摘要

我们给出了一种同构性测试，它可以在所有 n 顶点图（不包括作为拓扑子图的某个 h 顶点图）上以 \(n^{\operatorname{polylog}(h)} \) 的时间运行。之前的结果表明，此类图的同构性可以在 \(n^{\operatorname{polylog}(n)} \) （Babai，STOC 2016）和 nf(h) 的时间内对某个函数 f 进行测试（Grohe 和 Marx，SIAM J. Comp.，2015）。我们的结果还统一并扩展了之前针对最大度为 d 的图在时间 \(n^{\operatorname{polylog}(d)} \) 内运行的同构检验（SIAM J. Comp., 2023），以及针对哈德维格数为 h 的图在时间 \(n^{\operatorname{polylog}(h)} \) 内运行的同构检验（SIAM J. Comp., 2023）。

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Isomorphism Testing for Graphs Excluding Small Topological Subgraphs

We give an isomorphism test that runs in time \(n^{\operatorname{polylog}(h)} \) on all n-vertex graphs excluding some h-vertex graph as a topological subgraph. Previous results state that isomorphism for such graphs can be tested in time \(n^{\operatorname{polylog}(n)} \) (Babai, STOC 2016) and n^f(h) for some function f (Grohe and Marx, SIAM J. Comp., 2015).

Our result also unifies and extends previous isomorphism tests for graphs of maximum degree d running in time \(n^{\operatorname{polylog}(d)} \) (SIAM J. Comp., 2023) and for graphs of Hadwiger number h running in time \(n^{\operatorname{polylog}(h)} \) (SIAM J. Comp., 2023).

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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