A quasi-quadratic vertex-kernel for Cograph Edge Editing

We provide a O(k2logk) vertex kernel for cograph edge editing. This improves a cubic kernel found by Guillemot, Havet, Paul and Perez (Guillemot et al., 2010) which involved four reduction rules. We generalize one of their rules, based on packing of induced paths of length four, by introducing t-mod...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 357; pp. 282 - 296
Main Authors: Crespelle, Christophe, Pellerin, Rémi, Thomassé, Stéphan
Format: Journal Article
Language:English
Published: Elsevier B.V 15.11.2024
Elsevier
Subjects:
Cographs
Computer Science
Kernelization algorithms
Parameterized complexity
Cographs
68R10
05C85
Kernelization algorithms
Parameterized complexity
68Q27
ISSN:0166-218X
Online Access:Get full text
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Summary:We provide a O(k2logk) vertex kernel for cograph edge editing. This improves a cubic kernel found by Guillemot, Havet, Paul and Perez (Guillemot et al., 2010) which involved four reduction rules. We generalize one of their rules, based on packing of induced paths of length four, by introducing t-modules, which are modules up to t edge modifications. The key fact is that large t-modules cannot be edited more than t times, and this allows to obtain a near quadratic kernel. The extra logk factor seems tricky to remove as it is necessary in the combinatorial lemma on trees which is central in our proof. Nevertheless, we think that a quadratic bound should be reachable.
ISSN:0166-218X
DOI:10.1016/j.dam.2024.05.014