ALLSAT compressed with wildcards: Frequent Set Mining

Abstract: Like any simplicial complex the simplicial complex of all frequent sets can be compressed with wildcards once the maximal frequent sets (=facets) are known. Namely, the task (a particular kind of ALLSAT problem) is achieved by the author's recent algorithm Facets-To-Faces. But how to get the facets in the first place? The novel algorithm Find-All-Facets determines all facets of any (decidable) finite simplicial complex by replacing costly hypergraph dualization (Dualize+Advance and its variants) with the cheaper calculation of the minimal members of certain set families. The latter task is sped up by Vertical Layout. While all of this concerns arbitrary simplicial complexes, the impact to Frequent Set Mining (FSM) seems particularly high.