Neighborhood Inclusions for Minimal Dominating Sets Enumeration: Linear and Polynomial Delay Algorithms in P_7-Free and P_8-Free Chordal Graphs - Université Clermont Auvergne Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2019

Neighborhood Inclusions for Minimal Dominating Sets Enumeration: Linear and Polynomial Delay Algorithms in P_7-Free and P_8-Free Chordal Graphs

Résumé

In [M. M. Kanté, V. Limouzy, A. Mary, and L. Nourine. On the enumeration of minimal dominating sets and related notions. SIAM Journal on Discrete Mathematics, 28(4):1916-1929, 2014.] the authors give an O(n+m) delay algorithm based on neighborhood inclusions for the enumeration of minimal dominating sets in split and P_6-free chordal graphs. In this paper, we investigate generalizations of this technique to P_k-free chordal graphs for larger integers k. In particular, we give O(n+m) and O(n^3 * m) delays algorithms in the classes of P_7-free and P_8-free chordal graphs. As for P_k-free chordal graphs for k >= 9, we give evidence that such a technique is inefficient as a key step of the algorithm, namely the irredundant extension problem, becomes NP-complete.
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Dates et versions

hal-01786826 , version 1 (06-05-2018)
hal-01786826 , version 2 (29-11-2019)

Identifiants

  • HAL Id : hal-01786826 , version 2

Citer

Oscar Defrain, Lhouari Nourine. Neighborhood Inclusions for Minimal Dominating Sets Enumeration: Linear and Polynomial Delay Algorithms in P_7-Free and P_8-Free Chordal Graphs. 2019. ⟨hal-01786826v2⟩
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