CLOSURES OF DATABASE HYPERGRAPHS.

A hypergraph formalism is introduced to represent database schemata. In particular, a database schema B, described by one full join dependency and a set of functional dependencies, is represented by a (database) hypergraph H, containing both undirected and directed hyperedges. The closure of a database hypergraph is defined as the extension of the transitive closure of a graph. By using a lower bound and an upper bound of the hypergraph closure (called L-closure and U-closure, respectively), it is proved that two e-acyclic (e-independent) hypergraphs are equivalent if and only if they have the same closure. Moreover, a hypergraph is e-acyclic (e-independent) if and only if its closure is acyclic (independent) and, in most cases, such a recognition can be done in polynomial time. Finally, it is shown how to use the database hypergraph closure to solve some database design problems.