Date : Sept. 2, 2020, 9 a.m. - DEFRAIN Oscar - Amphi recherche pôle physique
On the dualization problem in graphs, hypergraphs, and lattices
This thesis deals with enumeration problems and algorithms.
We are interested in the complexity of the dualization of monotone Boolean functions through the different shapes it takes in graphs, hypergraphs, and lattices. In particular in this talk, we will consider the enumeration of minimal dominating sets in graphs, and will present new output-polynomial time algorithms to solve the problem in graphs without large cliques, as well as in some other related graph classes. In a second part, we will consider a natural generalization of this problem in lattices, and will review the recent progress on the problem. The presentation will end with different perspectives on the dualization problem in these structures. Access: http://www.recherche-environnement.univ-bpclermont.fr/wp/wp-content/uploads/2015/11/cezeaux-pole-physique.png
Jury: Nadia CREIGNOU (Pr, Université Aix Marseille) reviewer Sergei KUZNETSOV (Pr, Higher School of Economics, Moscow) reviewer Kazuhisa MAKINO (Pr, Reasearch Institute of Math. Sciences, Kyoto) reviewer Victor CHEPOI (Pr, Université Aix Marseille) examiner Arnaud DURAND (Pr, Université Paris Diderot) examiner Aurélie LAGOUTTE (MCF, UCA) examiner Lhouari NOURINE (Pr, UCA) supervisor