Relational-Database-Design-BCNF

• For the case of a decomposition of into and is lossless join if and only if at least one of the following dependencies is in :

• Let the schema is decomposed into .
• Let be the subset of dependencies that only includes attributes in for ,
• The decomposition is dependency preserving, if
  
• If the decomposition is not dependency preserving, then checking updates for violation of functional dependencies may require computing joins, which is expensive.

Example:


can be decomposed in two different ways

• • Lossless-join decomposition
    • Dependency preserving
• • Lossless-join decomposition
    • Not dependency preserving (cannot check without computing ⨝)