On the size of nonredundant FD-covers

Abstract

We investigate the relative size of equivalent nonredundant covers of functional dependencies. Let F and G denote two equivalent nonrebundant FD-covers on a set of attributes R. We show that |F| ⩽ |G|(|R| −1). As a consequence, the cardinality of any nonrebundant cover of functional dependencies differs by a factor of at most || − 1 from the cardinality of an equivalent minimum cover. We show that this bound is realizable. Let size(H) denote the number of attribute symbols used to express a cover H. We deduce the following relationship between the sizes of F and G: size(F) ⩽ size(G) × |R|(|R| − 1).