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The School of Data Analysis and Artificial Intelligence was created in 2014 as part of the Department of Data Analysis and Artificial Intelligence. The school consists of world-renowned researchers who actively participate in international research projects.
On September 2, 2020 at the University of Auvergne, PhD Defense Oscar Defrain presented his dissertation "On problems of dualization in graphs, hypergraphs and lattices".Abstract: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.Advisor: Lhouari NourineCommittee: Victor Chepoi, Nadia Creignou, Arnaud Durand, Sergei Kuznetsov, Aurélie Lagoutte, Kazuhisa Makino