on the dense families in the relational datamodel

In this paper, dense families of relation schemes are introduced. We characterize minimal keys of relation schemes in terms of dense families. Note that, the dense families of database relations were introduced by Jarvinen [6]. We prove that the set of all minimal keys of a relation scheme s= (U, F) is the transversal hypergraphs of a hypergraph D– {∅}, where Dis any s-dense family. We give a necessary and sufficient condition for an abitrary family to be s-dense family. We also present some dense families of relation schemes. Furthermore, in this paper, we also study antikeys by means of dense families. We present connections between antikeys and a dense family of relation schemes. Finally, we study the time complexity of the problem finding antikeys.