On some algorithmic aspects of hypergraphic matroids

Mourad Baïou (1) , Francisco Barahona (2)

1 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes
2 IBM Thomas J. Watson Research Center

Hypergraphics matroids were studied first by Lorea [18] and later by Frank et al [8]. They can be seen as generalizations of graphic matroids. Here we show that several algorithms developed for the graphic case can be extended to hypergraphic matroids. We treat the following: the separation problem for the associated polytope, testing independence, separation of partition inequalities, computing the rank of a set, computing the strength, computing the arboricity and network reinforcement.

Domaines: Intelligence artificielle [cs.AI]; Complexité [cs.CC]; Mathématique discrète [cs.DM]; Recherche opérationnelle [math.OC]; Combinatoire [math.CO]

Mourad Baïou, Francisco Barahona. On some algorithmic aspects of hypergraphic matroids. Discrete Mathematics, 2023, 346 (2), pp.113222. ⟨10.1016/j.disc.2022.113222⟩. ⟨hal-03872592⟩