Complete Decompositions of Join Dependencies

Abstract A join dependency is a necessary and sufficient condition for a decomposition of a relation schema into several relation schemata by relational algebra projection to have a lossless join. Such a condition can be described as a first-order formula known as a tuple-generating full dependency but its form varies according to how the schema is to be decomposed. Sometimes, a join dependency can be described as a conjunct of several simpler join dependencies and/or embedded join dependencies. Then, arises a problem to obtain all components of the given join dependency. This paper presents a way of decomposing the join dependency into product dependencies, multi-valued dependencies, polygonal dependencies and cross dependencies, and to reexamine join dependency inference rules in relation to such decompositions.