6 papers · 1 filter
Characterizing the optimum bases of a convex geometry using quasi-closed hypergraphs
Anthony Meunier, Lhouari Nourine, Simon Vilmin
Optimizing an implicational base of a closure system consists in turning this implicational base into an equivalent one with premises and conclusions as small as possible. This tas…
Generating minimal redundant and maximal irredundant sets in incidence graphs
Emanuel Castelo, Jérémie Chalopin, Oscar Defrain +1
It has been proved by Boros and Makino that there is no output-polynomial-time algorithm enumerating the minimal redundant sets or the maximal irredundant sets of a hypergraph, unl…
On the -base of Finite Lattices: Semidistributive, Modular, and Geometric Lattices
Kira Adaricheva, Simon Vilmin
Implicational bases are a well-known representation of closure spaces and their closure lattices. This representation is not unique, though, and a closure space usually admits mult…
Half-space separation in monophonic convexity
Mohammed Elaroussi, Lhouari Nourine, Simon Vilmin
We study half-space separation in the convexity of chordless paths of a graph, i.e., monophonic convexity. In this problem, one is given a graph and two (disjoint) subsets of verti…
Hierarchical decompositions of implicational bases for the enumeration of meet-irreducible elements
Lhouari Nourine, Simon Vilmin
We are interested in the problem of translating between two representations of closure systems, namely implicational bases and meet-irreducible elements. Albeit its importance, the…
On the preferred extensions of argumentation frameworks: bijections with naive sets
Mohammed Elaroussi, Lhouari Nourine, Mohammed Said Radjef +1
This paper deals with the problem of finding the preferred extensions of an argumentation framework by means of a bijection with the naive sets of another framework. First, we cons…