An Information-Theoretic Analysis of Relational Databases—Part II: Information Structures of Database Schemas

The structural properties of acyclic database schemas, especially the interrelationships between acyclic join dependencies and multivalued dependencies, are examined in this paper. The intersection closure of a database schema is a semilattice, which is usually represented by Hasse diagram in algebra. The Hasse diagram of a schema is analogous to the Bachman diagram of a network model. Based on the topological structures of Hasse diagrams, the acyclic join dependency is proved to be equivalent to a set of conflict-free multivalued dependencies. Furthermore, we show that if the Hasse diagram is loop free, then the corresponding set of multivalued dependencies is also contention-free. This result is consistent with previous results derived from the Bachman diagram.