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Isomorphism Testing Parameterized by Genus and Beyond

Author Daniel Neuen

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LIPIcs.ESA.2021.72.pdf
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ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
  • Theory of computation → Graph algorithms analysis
  • Mathematics of computing → Graphs and surfaces
Keywords
  • graph isomorphism
  • fixed-parameter tractability
  • Euler genus
  • Weisfeiler-Leman algorithm

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Abstract

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.

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Daniel Neuen. Isomorphism Testing Parameterized by Genus and Beyond. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 72:1-72:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ESA.2021.72

Author Details

Daniel Neuen
  • CISPA Helmholtz Center for Information Security, Saarland Informatics Campus, Saarbrücken, Germany

Funding

Research supported by the European Research Council (ERC) consolidator grant No. 725978 SYSTEMATICGRAPH.

References

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