Isomorphism Testing for Graphs Excluding Small Minors

IF 1.2 3区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

SIAM Journal on Computing Pub Date : 2023-02-28 DOI:10.1137/21m1401930

Martin Grohe, Daniel Neuen, Daniel Wiebking

引用次数: 0

Abstract

We prove that there is a graph isomorphism test running in time $n^{\operatorname{polylog}(h)}$ on $n$-vertex graphs excluding some $h$-vertex graph as a minor. Previously known bounds were $n^{\operatorname{poly}(h)}$ (Ponomarenko, 1988) and $n^{\operatorname{polylog}(n)}$ (Babai, STOC 2016). For the algorithm we combine recent advances in the group-theoretic graph isomorphism machinery with new graph-theoretic arguments.

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不包含小次的图的同构检验

我们证明了在$n^{\operatorname{polylog}(h)}$ n -顶点图上存在一个图同构测试，该测试在$n^{\operatorname{polylog}}$上运行，不包括$h$顶点图作为次要图。以前已知的边界是$n^{\operatorname{poly}(h)}$ (Ponomarenko, 1988)和$n^{\operatorname{polylog}(n)}$ (Babai, STOC 2016)。对于该算法，我们将群论图同构机制的最新进展与新的图论论证结合起来。

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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来源期刊

SIAM Journal on Computing 工程技术-计算机：理论方法

CiteScore

4.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

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.