eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-08-31
72:1
72:18
10.4230/LIPIcs.ESA.2021.72
article
Isomorphism Testing Parameterized by Genus and Beyond
Neuen, Daniel
1
https://orcid.org/0000-0002-4940-0318
CISPA Helmholtz Center for Information Security, Saarland Informatics Campus, Saarbrücken, Germany
We present an isomorphism test for graphs of Euler genus g running in time 2^{{O}(g⁴ log g)}n^{{O}(1)}. Our algorithm provides the first explicit upper bound on the dependence on g for an fpt isomorphism test parameterized by the Euler genus of the input graphs. The only previous fpt algorithm runs in time f(g)n for some function f (Kawarabayashi 2015). Actually, our algorithm even works when the input graphs only exclude K_{3,h} 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, we introduce (t,k)-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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol204-esa2021/LIPIcs.ESA.2021.72/LIPIcs.ESA.2021.72.pdf
graph isomorphism
fixed-parameter tractability
Euler genus
Weisfeiler-Leman algorithm