What are the properties of decomposition of a database relation? Explain.

Concept

A decomposition replaces a relation schema R with smaller schemas R1, R2, ..., Rn whose combined attributes cover R. A good decomposition should remove redundancy and update anomalies without losing information or enforceable constraints.

Its core tests are attribute preservation, lossless join, and dependency preservation; a well-designed normalization also aims to minimize repeated information.

Application

• Attribute preservation: Every attribute of R occurs in at least one component, so the union of the component attribute sets equals R.

• Lossless-join (non-additive) property: For every valid instance r of R, the natural join of its projections onto R1, R2, ..., Rn reconstructs exactly r. It neither loses tuples nor creates spurious tuples.

• Dependency preservation: The dependencies projected onto the component schemas collectively imply the original dependency set F. Therefore, the constraints can be checked on the smaller relations without joining them first.

• Minimal redundancy: The decomposition should place the schemas in suitable normal forms so that repeated facts and insertion, update, and deletion anomalies are reduced.

Cross-check

• These tests are independent: a decomposition can be lossless yet fail to preserve all dependencies, or preserve dependencies yet be lossy.

• BCNF decomposition guarantees lossless joins but may sacrifice dependency preservation, whereas a standard 3NF synthesis can preserve dependencies and remain lossless.

Thus, an acceptable decomposition preserves all attributes, reconstructs the original relation without spurious data, preserves constraints, and reduces redundancy.