A minimal base or a direct base? That is the question!

Abstract: In this paper we revisit the problem of computing the closure of a set of attributes given a basis of dependencies or implications. This problem is of main interest in logics, in the relational database model, in lattice theory, and in Formal Concept Analysis as well. A basis of dependencies may have different characteristics, among which being minimal'', e.g., the Duquenne-Guigues Basis, or beingdirect'', e.g., the the Canonical Basis and the D-basis. Here we propose an extensive and experimental study of the impacts of minimality and directness on the closure algorithms. The results of the experiments performed on real and synthetic datasets are analyzed in depth, and suggest a different and fresh look at computing the closure of a set of attributes w.r.t. a basis of dependencies. This paper has been submitted to the International Journal of Approximate Reasoning.