Ensuring the Existence of a BCNF-Decomposition that Preserves Functional Dependencies in O(N²) Time

In the design theory for the relational data base model [6] the decomposition of a relation scheme according to some normal form has been advocated for as one means to avoid undesired redundancy and anomalies [7,8,16]. Desired characteristics of such a decomposition in the case of a relation scheme R with an associated set F of functional dependencies are the lossless-join property and the preservation of functional dependencies [13,16]. Every relation scheme R with an associated set F of functional dependencies has a decomposition into third normal form (3NFl that has the loss-less-join property and preserves functional dependencies [41. However, for a relation scheme R with an associated set F of functional dependencies, a decomposition into Boyce-Codd normal form (BCNF) that has the lossless-join property and preserves functional dependencies does not always exist. Beeri and Bernstein [3] have shown, that, given a relation scheme R and a set F of functional dependen-