Finding an Optimal Cover for a Kind of Set of Functional Dependencies in Polynomial Time

A smaller cover makes numerous algorithms (e.g., the classic synthesizing algorithm) need less storage space and less run time. Maier proves that the problem of finding an optimal cover (possible fewest attributes) is NP-complete. For a single-ended set of functional dependencies (the left side of every functional dependency has a single attribute), it is shown here that the optimal cover of a single-ended set of functional dependencies can be found in polynomial time, using the notion of mini cover. A simplified graphical representation (FD-graph) for a set of functional dependencies is introduced. It is provable that the transitive reduction of the FD-graph of a single-ended set of functional dependencies can be transformed into corresponding mini cover and further optimal cover.