Isomorphism Testing Parameterized by Genus and Beyond

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-01-22 DOI:10.1137/22m1514076

Daniel Neuen

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 453-484, March 2024.
Abstract. We present an isomorphism test for graphs of Euler genus [math] running in time [math]. Our algorithm provides the first explicit upper bound on the dependence on [math] for an fpt isomorphism test parameterized by the Euler genus of the input graphs. The only previous fpt algorithm runs in time [math] for some function [math] (Kawarabayashi 2015). Actually, our algorithm even works when the input graphs only exclude [math] as a minor. For such graphs, no fpt isomorphism test was known before. The algorithm builds on an elegant combination of simple group-theoretic, combinatorial, and graph-theoretic approaches. In particular, our algorithm relies on the notion of [math]-WL-bounded graphs which provide a powerful tool to combine group-theoretic techniques with the standard Weisfeiler–Leman algorithm. This concept may be of independent interest.

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同构测试以属类及其他参数为参数

SIAM 离散数学杂志》，第 38 卷，第 1 期，第 453-484 页，2024 年 3 月。摘要。我们提出了一种在[math]时间内运行的欧拉属[math]图同构检验。我们的算法首次明确了以输入图的欧拉属为参数的 fpt 同构检验对 [math] 的依赖上限。之前唯一的 fpt 算法在某个函数 [math] 的 [math] 时间内运行（Kawarabayashi 2015）。实际上，我们的算法甚至可以在输入图只排除[math]这个次要函数的情况下运行。对于这样的图，以前还没有任何 fpt 同构检验方法。该算法建立在简单的群论、组合和图论方法的优雅结合之上。特别是，我们的算法依赖于[math]-WL-bounded graphs（[math]-WL-边界图）的概念，它为将群论技术与标准 Weisfeiler-Leman 算法相结合提供了一个强大的工具。这一概念可能具有独立的意义。

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 Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.