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Association algebra: a mathematical foundation for object-oriented databases

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3 Author(s)
Su, S.Y.W. ; Database Syst. Res. & Dev. Center, Florida Univ., Gainesville, FL, USA ; Guo, M. ; Lam, H.

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

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Knowledge and Data Engineering, IEEE Transactions on  (Volume:5 ,  Issue: 5 )