  This work is part of the field of the hypergraph theory and focuses on
hypergraph minimal transversal. The problem of extracting the minimal
transversals from a hypergraph received the interest of many researchers as
shown the number of algorithms proposed in the literature, and this is mainly
due to the solutions offered by the minimal transversal in various application
areas such as databases, artificial intelligence, e-commerce, semantic web,
etc. In view of the wide range of fields of minimal transversal application and
the interest they generate, the objective of this thesis is to explore new
application paths of minimal transversal by proposing methods to optimize the
extraction. This has led to three proposed contributions in this thesis. The
first approach takes advantage of the emergence of Web 2.0 and, therefore,
social networks using minimal transversal for the detection of important actors
within these networks. The second part of research in this thesis has focused
on reducing the number of hypergraph minimal transversal. A concise and
accurate representation of minimal transversal was proposed and is based on the
construction of an irredundant hypergraph, hence are calculated the irredundant
minimal transversal of the initial hypergraph. An application of this
representation to the dependency inference problem is presented to illustrate
the usefulness of this approach. The last approach includes the hypergraph
decomposition into partial hypergraph the local minimal transversal are
calculated and their Cartesian product can generate all the hypergraph
transversal sets. Different experimental studies have shown the value of these
proposed approaches.
