Join

Definition

The join is a binary operator of the relational algebra that combines tuples of different relations based on a relationship between values of their attributes. The primitive version of the join operator is called natural join. Given two relation instances R ₁, over set of attributes U ₁, and R ₂ over set of attributes U ₂, the natural join R ₁ ⋈ R ₂ returns a new relation, over set of attributes U ₁ ∪ U ₂, consisting of tuples {t |t(U ₁) ∈ R ₁ and t(U ₂) ∈ R ₂}. Here t(U) denotes the restriction of the tuple t to attributes in the set U.

A derivable version of the join operator is obtained by composing the natural join with the selection operator σ: the theta join R ₁ ⋈ _θ R ₂ is defined as σ _θ (R ₁ ⋈ R ₂), where θ is an arbitrary condition allowed in a generalized selection over set of attributes U ₁ ∪ U ₂. In the case that θ is a conjunction of equality atoms of the form A = B, where A is an attribute in U ₁ and B an attribute in U ₂, the theta join is called equijoin.

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