Minimal dominating sets enumeration with FPT-delay parameterized by the degeneracy and maximum degree - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2023

Minimal dominating sets enumeration with FPT-delay parameterized by the degeneracy and maximum degree

Résumé

At STOC 2002, Eiter, Gottlob, and Makino presented a technique called ordered generation that yields an $n^{O(d)}$-delay algorithm listing all minimal transversals of an $n$-vertex hypergraph of degeneracy $d$, for an appropriate definition of degeneracy. Recently at IWOCA 2019, Conte, Kanté, Marino, and Uno asked whether, even for a more restrictive notion of degeneracy, this XP-delay algorithm parameterized by $d$ could be made FPT-delay parameterized by $d$ and the maximum degree $\Delta$, i.e., an algorithm with delay $f(d, \Delta) \cdot n^{O(1)}$ for some computable function $f$. We answer this question in the affirmative whenever the hypergraph corresponds to the closed neighborhoods of a graph, i.e., we show that the intimately related problem of enumerating minimal dominating sets in graphs admits an FPT-delay algorithm parameterized by the degeneracy and the maximum degree.
Fichier principal
Vignette du fichier
arXiv.pdf (595.01 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04162863 , version 1 (16-07-2023)

Identifiants

  • HAL Id : hal-04162863 , version 1

Citer

Valentin Bartier, Oscar Defrain, Fionn Mc Inerney. Minimal dominating sets enumeration with FPT-delay parameterized by the degeneracy and maximum degree. 2023. ⟨hal-04162863⟩
21 Consultations
36 Téléchargements

Partager

More