---

Heuristic 2 for finding keys

---

• Heuristic 2: Find all keys - find the necessary attributes first
  • Problem:

    Find all keys in the following relations:

    R(A, B, C, D, E, F) ℉ = { A → BC BD → EF F → A }

    ---

    ---

  • Heuristic

    Find the irreplaceable attributes An attribute is replaceable if it appears in the RHS of some functional dependency A key must include every irreplaceable attribute The base set is the set of all irreplaceable attributes Add other attributes to the base set until you have a key

    ---

  • Example:

    R(A, B, C, D, E, F) ℉ = { A → BC BD → EF F → A } Find the irreplaceable attributes Irreplaceable: D The base set is the set of all irreplaceable attributes Base set = { D } Add other attributes to the base set until you have a key Add 1 attribute from: A, B, C, E, F +A: AD+ = ABCDEF ... key ! +B: BD+ = ABCDEF ... key ! +C: CD+ = CD +E: DE+ = DE +F: DF+ = ABCDEF ... key ! Conclusion: AD, BD, DF are keys Add 2 attributes (do NOT expand with a KNOWN key I.e.: Do NOT include A, B, F) ) Select 2 attributes from: C, E CDE+ = CDE Add 3 attributes (do NOT expand a KNOWN key I.e.: Do NOT include A, B, F) ) Select 3 attributes from: C, E Impossible - DONE.

    ---

    ---

    ---

  • The keys of relation R are:

    AD, BD and DF