eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-03-06
7:1
7:13
10.4230/LIPIcs.STACS.2017.7
article
Parameterized Complexity of Small Weight Automorphisms
Arvind, Vikraman
Köbler, Johannes
Kuhnert, Sebastian
Torán, Jacobo
We show that checking if a given hypergraph has an automorphism that moves exactly k vertices is fixed parameter tractable, using k and additionally either the maximum hyperedge size or the maximum color class size as parameters. In particular, it suffices to use k as parameter if the hyperedge size is at most polylogarithmic in the size of the given hypergraph.
As a building block for our algorithms, we generalize Schweitzer's FPT algorithm [ESA 2011] that, given two graphs on the same vertex set and a parameter k, decides whether there is an isomorphism between the two graphs that moves at most k vertices. We extend this result to hypergraphs, using the maximum hyperedge size as a second parameter.
Another key component of our algorithm is an orbit-shrinking technique that preserves permutations that move few points and that may be of independent interest. Applying it to a suitable subgroup of the automorphism group allows us to switch from bounded hyperedge size to bounded color classes in the exactly-k case.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol066-stacs2017/LIPIcs.STACS.2017.7/LIPIcs.STACS.2017.7.pdf
Parameterized algorithms
hypergraph isomorphism.