The application of the object-oriented (O-O) paradigm in the database management field has gained much attention in recent years. Several experimental and commercial O-O database management systems have become available. However, the existing O-O DBMSs still lack a solid mathematical foundation for the manipulation of O-O databases, the optimization of queries, and the design and selection of storage structures for supporting O-O database manipulations. This paper presents an association algebra (A-algebra) to serve as a mathematical foundation for processing O-O databases, which is analogous to the relational algebra used for processing relational databases. In this algebra, objects and their associations in an O-O database are uniformly represented by association patterns which are manipulated by a number of operators to produce other association patterns. Different from the relational algebra, in which set operations operate on relations with union-compatible structures, the A-algebra operators can operate on association patterns of homogeneous and heterogeneous structures. Different from the traditional record-based relational processing, the A-algebra allows very complex patterns of object associations to be directly manipulated. The pattern-based query formulation and the A-algebra operators are described. Some mathematical properties of the algebraic operators are presented together with their application in query decomposition and optimization. The completeness of the A-algebra is also defined and proven. The A-algebra has been used as the basis for the design and implementation of an object-oriented query language, OQL, which is the query language used in a prototype Knowledge Base Management System OSAM*.KBMS.>

An association algebra (A-algebra) is presented for manipulating object-oriented (O-O) databases which is analogous to the relational algebra for relational databases. In this algebra, objects and their associations in an O-O database are uniformly represented by association patterns and are manipulated by a number of operators. These operators are defined to operate on association patterns of both heterogeneous and homogeneous structures. Very complex structures (e.g. network structures of object associations across several classes) can be directly manipulated by these operators. Therefore, the association algebra has greater expressive powers than the relational algebra which manipulates on relations of compatible structures. Some mathematical properties of these operators are described together with their application in query decomposition and optimization. The algebra has been used as the basis for the design and implementation of an O-O query language called OQL and a knowledge rule specification language.>