Article Dans Une Revue Theoretical Computer Science Année : 2023

The enumeration of meet-irreducible elements based on hierarchical decompositions of implicational bases

Résumé

We study the well-known problem of translating between two representations of closure systems, namely implicational bases and meet-irreducible elements. Albeit its importance, the problem is open. In this paper, we introduce splits of an implicational base. It is a partitioning operation of the implications which we recursively apply to obtain a binary tree representing a decomposition of the implicational base. We show that this decomposition can be conducted in polynomial time and space in the size of the input implicational base. Focusing on the case of acyclic splits, we obtain a recursive characterization of the meetirreducible elements of the associated closure system. We use this characterization and hypergraph dualization to derive new results for the translation problem in acyclic convex geometries.

Fichier principal
Vignette du fichier
arxiv.pdf (1.34 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-03565763 , version 1 (11-02-2022)

Licence

Identifiants

Citer

Lhouari Nourine, Simon Vilmin. The enumeration of meet-irreducible elements based on hierarchical decompositions of implicational bases. Theoretical Computer Science, 2023, 969, pp.114030. ⟨10.1016/j.tcs.2023.114030⟩. ⟨hal-03565763⟩
228 Consultations
538 Téléchargements

Altmetric

Partager

  • More