The complete extraction of local patterns in binary relations was
extensively studied, in particular by our team. Its applications are
both numerous and fruitful (e.g., log compression, search for
synexpression groups, analysis of the gene regulation
mechanisms). Looking beyond the strict framework of closed sets enable
to tackle new problems such as the analysis of dynamic interaction
graphs or the extraction of fault-tolerant patterns.

Generalizing the notion of closed sets to n-ary relations is a first
step on this way. The main difficulty consists in designing complete
solvers which are able, in practice, to extract these patterns in
large data sets. Real data being often noisy, the conceptual framework
of closed sets gains by being extended to take into account
fault-tolerant contexts. In addition, focusing on the particularities
of dynamic interaction graphs (two symmetric dimensions and an ordered
one) enables significant improvements in their analysis.