文章基本信息

标题：Hypergraph Isomorphism for Groups with Restricted Composition Factors
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作者：Daniel Neuen
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：168
页码：88:1-88:19
DOI：10.4230/LIPIcs.ICALP.2020.88
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We consider the isomorphism problem for hypergraphs taking as input two hypergraphs over the same set of vertices V and a permutation group Î" over domain V, and asking whether there is a permutation Î³ â^^ Î" that proves the two hypergraphs to be isomorphic. We show that for input groups, all of whose composition factors are isomorphic to a subgroup of the symmetric group on d points, this problem can be solved in time (n+m)^O((log d)^c) for some absolute constant c where n denotes the number of vertices and m the number of hyperedges. In particular, this gives the currently fastest isomorphism test for hypergraphs in general. The previous best algorithm for the above problem due to Schweitzer and Wiebking (STOC 2019) runs in time n^O(d)m^O(1). As an application of this result, we obtain, for example, an algorithm testing isomorphism of graphs excluding K_{3,h} as a minor in time n^O((log h)^c). In particular, this gives an isomorphism test for graphs of Euler genus at most g running in time n^O((log g)^c).
关键词：graph isomorphism; groups with restricted composition factors; hypergraphs; bounded genus graphs