Multivalued Dependencies are helps to lossless decomposition and form relation R based on trivial multivalued dependencies. An instance, a relation R(A B C) is decomposed into relation R1(A B) and R2(A C) based on trivial A ® B multivalued functional dependencies.
Join Dependency is helps to lossless decomposition and form relation R based on nontrivial multivalued dependencies. An instance, a relation R(A B C) is decomposed into relation R1(A B), R2(B C) and R3(A C) based on nontrivial multivalued functional dependencies.
Let R = {R1, R2, ..., Rn} be a set of relation schemes over union, the relation r(R) satisfies the join dependency * [R1, R2, ..., Rn] if r decomposes lossless onto R1, R2, ... Rn.
That is, r = pR1(r) ⋈pR2(r) ⋈ ..., ⋈pRn(r).
A join dependency * [R1, R2, ..., Rn] over R is trivial if it is satisfied by every relation r(R).