Decomposition of a relation scheme into Boyce-Codd Normal Form

Decomposition into Boyce-Codd Normal Form (BCNF) with a lossless join and preservation of dependencies is desired in the design of a relational database scheme. However, there may be no decomposition of a relation scheme into BCNF that is dependency preserving, and the known algorithms for lossless join decomposition into BCNF require exponential time and space. In this paper we give an efficient algorithm for lossless join decomposition and show that the problem of deciding whether a relation scheme has a dependency-preserving decomposition into BCNF is NP-hard. The algorithm and the proof assume that all data dependencies are functional. We then discuss the extension of our techniques to the case where data dependencies are multivalued.