Minimum covers in the relational database model (Extended Abstract)

Numerous algorithms concerning relational databases use a cover for a set of functional dependencies as all or part of their input. Examples are Bernstein and Beeri's synthesis algorithm [BB] and the tableau modification algorithm of Aho, Beeri, and Ullman [ABU]. The performance of these algorithms may depend both on the number of functional dependencies in the cover and the total size of the cover. Starting with a smaller cover will make such algorithms run faster. After Bernstein [Be75], many researchers believe the problem of finding a minimum cover is NP-complete. We show that minimum covers can be found in polynomial time, using the notion of direct determination. The proof details the structure of minimum covers, refining the structure Bernstein and Beeri show for non-redundant covers [BB]. The kernel algorithm of Lewis, Sekino, and Ting [LST] is improved using these results.