Generalized domination in closure systems

Authors:
Anne Berry;Eric SanJuan;Alain Sigayret
Affiliations:
LIMOS (CNRS UMR 6158), Université Blaise Pascal, Ensemble Scientifique des Cézeaux, 63173 Aubière cedex, France;LITA (EA 3097), Université Paul Verlaine de Metz, Ile du Saulcy, 57045 Metz cedex 1, France;LIMOS (CNRS UMR 6158), Université Blaise Pascal, Ensemble Scientifique des Cézeaux, 63173 Aubière cedex, France
Venue:
Discrete Applied Mathematics - Special issue: Discrete mathematics & data mining II (DM & DM II)
Year:
2006

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Abstract

In the context of extracting maximal item sets and association rules from a binary data base, the graph-theoretic notion of domination was recently used to characterize the neighborhood of a concept in the corresponding lattice. In this paper, we show that the notion of domination can in fact be extended to any closure operator on a finite universe and be efficiently encoded into propositional Horn functions. This generalization enables us to endow notions and algorithms related to Formal Concept Analysis with Horn minimization and minimal covers of functional dependencies in Relational Databases.