{"title":"Isomorphism Testing Parameterized by Genus and Beyond","authors":"Daniel Neuen","doi":"10.1137/22m1514076","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 453-484, March 2024. <br/> 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.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/22m1514076","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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.
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