Algorithms for k-meet-semidistributive lattices - Université Clermont Auvergne Accéder directement au contenu
Article Dans Une Revue Theoretical Computer Science Année : 2017

Algorithms for k-meet-semidistributive lattices

Résumé

In this paper we consider k-meet-semidistributive lattices and we are interested in the computation of the set-colored poset associated to an implicational base. The parameter k is of interest since for any finite lattice L there exists an integer k for which L is k-meet-semidistributive. When k=1 they are known as meet-semidistributive lattices.We first give a polynomial time algorithm to compute an implicational base of a k-meet-semidistributive lattice from its associated colored poset. In other words, for a fixed k, finding a minimal implicational base of a k-meet-semidistributive lattice L from a context (FCA literature) of L can be done not just in output-polynomial time (which is open in the general case) but in polynomial time in the size of the input. This result generalizes that in [26]. Second, we derive an algorithm to compute a set-colored poset from an implicational base which is based on the enumeration of minimal transversals of a hypergraph and turns out to be in polynomial time for k-meet-semidistributive lattices [13,20]. Finally, we show that checking whether a given implicational base describes a k-meet-semidistributive lattice can be done in polynomial time.
Fichier principal
Vignette du fichier
meet_sd.pdf (269.88 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01571243 , version 1 (01-08-2017)

Identifiants

Citer

Laurent Beaudou, Arnaud Mary, Lhouari Nourine. Algorithms for k-meet-semidistributive lattices. Theoretical Computer Science, 2017, 658, pp.391 - 398. ⟨10.1016/j.tcs.2015.10.029⟩. ⟨hal-01571243⟩
197 Consultations
217 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More