Join Dependency

Synonyms

JD

Definition

A join dependency (JD) over a relation schema R[U] is an expression of the form ®[X₁,…,X_n], where X₁ ∪ … ∪ X_n = U. An instance I of R[U] satisfies ®[X₁,…,X_n] if $I={\pi}_{X_1}(I)\ddot{\mathrm{I}}\dots \ddot{\mathrm{I}}{\pi}_{X_n}(I)$. In other words, an instance satisfies the join dependency if it is equal to the join of its projections on the sets of attributes X₁,…,X_n. A multivalued dependency X→→Y is a special case of a join dependency on two sets, and can be expressed as ⋈ [XY, X(U − XY)] where XY representsX ∪ Y.

Key Points

Join dependencies are particularly important in connection with the decomposition technique for schema design and normalization. The main goal of the decomposition technique is to avoid redundancies due to data dependencies by decomposing a relation into smaller parts. A good decomposition should have the lossless joinproperty, meaning that no information should be lost after the decomposition. In other words, the original database...