Criteria
Lossless join can also be called nonadditive. If is split into and , for this decomposition to be lossless (i.e., ) then at least one of the two following criteria should be met.Check 1: Verify join explicitly
Projecting on and , and joining them back, results in the relation you started with.Check 2: Via functional dependencies
Let be a relation schema. Let be a set of functional dependencies on . Let and form a decomposition of . The decomposition is a lossless-join decomposition of if at least one of the following functional dependencies are in + (where + stands for the closure for every attribute or attribute sets in ): * *Examples
* Let be the relation schema, with attributes , , and . * Let be the set of functional dependencies. * Decomposition into and is lossless under because . is a superkey in , meaning we have a functional dependency . In other words, now we have proven that .References
{{Reflist Databases Data modeling Database constraints Database normalization Relational algebra