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Mathemtical Model of Composite Objects and Its Application for Organizing Engineering Databases
January 1988 (vol. 14 no. 1)
pp. 71-84

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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Index Terms:
database partitioning; composite objects; engineering databases; clustering concept; component aggregation; assemblies; equivalent objects; equivalence classes; Boolean algebra; minterms; stored views; relational database; design data; frequent access patterns; CAD; data structures; database theory; relational databases
M.A. Ketabchi, V. Berzins, "Mathemtical Model of Composite Objects and Its Application for Organizing Engineering Databases," IEEE Transactions on Software Engineering, vol. 14, no. 1, pp. 71-84, Jan. 1988, doi:10.1109/32.4624
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