Normalization Using Join Dependencies Join dependencies constrain the set of legal relations over a schema R to those relations for which a given decomposition is a lossless-join decomposition. Let R be a relation schema and R1,R2,...,Rn be a decomposition of R.If R= RR2....R,we say that a relation r(R)satisfies the join dependency *(R1,R2...Rn)if: r=R1()凶ΠR2(0凶..凶ΠRn() Ajoin dependency is trivial if one of the R,is R itself. Ajoin dependency *(R1,R2)is equivalent to the multivalued dependency R1 R2 R2.Conversely,a B is equivalent to *(a(R-B),aB) However,there are join dependencies that are not equivalent to any multivalued dependency. Database System Concepts,5th Ed. C.7 ©Silberschat乜，Korth and SudarshanDatabase System Concepts, 5 C.7 ©Silberschatz, Korth and Sudarshan th Ed. Normalization Using Join Dependencies Join dependencies constrain the set of legal relations over a schema R to those relations for which a given decomposition is a lossless-join decomposition. Let R be a relation schema and R1 , R2 ,..., Rn be a decomposition of R. If R = R1  R2  ….  Rn , we say that a relation r(R) satisfies the join dependency *(R1 , R2 ,..., Rn ) if: r =R1 (r) ⋈ R2 (r) ⋈ …… ⋈ Rn(r) A join dependency is trivial if one of the Ri is R itself. A join dependency *(R1 , R2 ) is equivalent to the multivalued dependency R1  R2 R2 . Conversely,   is equivalent to *( (R - ),   ) However, there are join dependencies that are not equivalent to any multivalued dependency