Mathematical Model of Composite Objects and Its Application for Organizing Engineering Databases

The authors introduce a clustering concept called component aggregation which considers assemblies having the same types of parts as equivalent objects. The notion of equivalent objects is used to develop a mathematical model of composite objects. It is shown that the set of equivalence classes of objects form a Boolean algebra whose minterms represent the objects that are not considered composite at the current viewing level. The algebraic structure of composite objects serves as a basis for developing a technique for organizing composite objects and supporting materialization of explosion views. The technique provides a clustering mechanism which partitions the database into meaningful and application-oriented clusters, and allows any desired explosion view to be materialized using a minimal set of stored views. A simplified relational database for design data and a set of frequent access patterns in design applications are outlined and used to demonstrate the benefits of database organizations based on the mathematical model of composite objects. >

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