Object-oriented database schema analysis and inheritance processing: A graph-theoretic approach

Abstract

In this paper we address the inheritance process in the context of strongly typed Object-oriented database (OODB) systems, allowing multiple inheritance and overriding. For such powerful systems, it is important to analyse the inheritance hierarchy to identify a number of significant properties. The first, schema consistency, is connected to the inheritance conflicts. In the presence of an unsolvable inheritance conflict there is a contradiction in the schema. The second property is related to the termination of the inheritance process. We expect that all the subtypes in the schema, if consistent, can be rewritten in expanded form, after inheritance, in a finite time. Schemas that guarantee these two formal properties will be referred to as correct schemas. In the paper a graph-theoretic method is provided, aimed at supporting the designer in checking the correctness and deriving the expanded form of a schema. Furthermore, from the analysis of the complexity of the inheritance process, a third formal property has been defined, concerning the degree of compactness achievable in a schema, by using inheritance hierarchies. In particular, a class of schemas has been defined, referred to as logarithmic schemas, whose expanded forms, after inheritance, become exponential in the size of the original schemas.