5 papers
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…
Enumerating minimal dominating sets in the (in)comparability graphs of bounded dimension posets
Marthe Bonamy, Oscar Defrain, Piotr Micek +1
Enumerating minimal transversals in a hypergraph is a notoriously hard problem. It can be reduced to enumerating minimal dominating sets in a graph, in fact even to enumerating min…
Computing the -base and -relation in finite closure systems
Kira Adaricheva, Lhouari Nourine, Simon Vilmin
Implicational bases (IBs) are a common representation of finite closure systems and lattices, along with meet-irreducible elements. They appear in a wide variety of fields ranging…
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…
Towards declarative comparabilities: application to functional dependencies
Lhouari Nourine, Jean Marc Petit, Simon Vilmin
In real life, data are often of poor quality as a result, for instance, of uncertainty, mismeasurements, missing values or bad inputs. This issue hampers an implicit yet crucial op…