Minimal Instances of Database Schemes with Additive Cardinality Constraints

In the entity-relationship approach to database design, integrity constraints are used to express database semantics. Cardinality constraints are a frequently used way of imposing restrictions to the structure of the databases. In this paper, we consider additive cardinality constraints which specify lower and upper bounds on the total number of relationships an entity of a xed type may be involved in. It is natural to ask for the smallest fully-populated database that yields a given set of integrity constraints. For additive cardinality constraints this proplem is proved to be NP-complete. However, the problem can be tackled via branch & bound. To solve the relaxed optimization problem we use min-cost ow methods in a suitable network depending on the given database scheme.