Split-freedom and MVD-intersection: A new characterization of multivalued dependencies having conflict-free covers

Abstract

Sets of multivalued dependencies (MVDs) having conflict-free covers are important to the theory and design of relational databases [Li, Sc1, Sc2, BFMY]. Their desirable properties motivate the problem of testing a set M of MVDs for the existence of a conflict-free cover. In [GT1] Goodman and Tay have proposed an approach based on the possible equivalence of M to a single (acyclic) join dependency (JD). We remark that their characterization does not lend an insight into the nature of such sets of MVDs. Here, we use notions that are intrinsic to MVDs to develop a new characterization. Our approach proceeds in two stages. In the first stage, we use the notion of "split-free" sets of MVDs and obtain a characterization of sets M of MVDs having split-free covers. In the second, we use the notion of "intersection" of MVDs to arrive at a necessary and sufficient condition for a split-free set of MVDs to be conflict-free. Based on our characterizations, we also give polynomial time algorithms for testing whether M has split-free and conflict-free covers. The highlight of our approach is the clear insight it provides into the nature of sets of MVDs having conflict-free covers. Less emphasis is given in this paper to the actual efficiency of the algorithms. Finally, as a bonus, we derive a desirable property of split-free sets of MVDs, thereby showing that they are interesting in their own right.