1. Relational Design Theory
Multivalued Dependencies &
4th Normal Form

2. Relational design by decomposition
MVDs & 4NF
Relational design by decomposition
“Mega” relations + properties of the data
System decomposes based on properties
Final set of relations satisfies normal form
No anomalies, no lost information
Functional dependencies  Boyce-Codd Normal Form
Multivalued dependences  Fourth Normal Form

3. Example: College application info. FDs? Keys? BCNF? Good design?
MVDs & 4NF
Example: College application info.
Apply(SSN, cName, hobby)
FDs?
Keys?
BCNF?
Good design?

4. Multivalued Dependency
MVDs & 4NF
Multivalued Dependency
Based on knowledge of real world
All instances of relation must adhere

5. MVDs & 4NF
Apply(SSN, cName, hobby)

6. Modified example MVDs? Good design? MVDs & 4NF
Apply(SSN, cName, hobby)
Reveal hobbies to colleges selectively
MVDs?
Good design?

7. Expanded example MVDs & 4NF Apply(SSN, cName, date, major, hobby)
Reveal hobbies to colleges selectively
Apply once to each college
May apply to multiple majors

8. Trivial Multivalued Dependency Nontrivial MVD
MVDs & 4NF
Trivial Multivalued Dependency
Nontrivial MVD

9. Rules for Multivalued Dependencies FD-is-an-MVD rule
MVDs & 4NF
Rules for Multivalued Dependencies
FD-is-an-MVD rule

10. Rules for Multivalued Dependencies Intersection rule Transitive rule
MVDs & 4NF
Rules for Multivalued Dependencies
Intersection rule
Transitive rule

11. Fourth Normal Form MVDs & 4NF Relation R with MVDs is in 4NF if:
For each nontrivial A B, A is a key

12. Fourth Normal Form MVDs & 4NF Relation R with MVDs is in 4NF if:
For each nontrivial A B, A is a key

13. 4NF decomposition algorithm
MVDs & 4NF
4NF decomposition algorithm
Input: relation R + FDs for R + MVDs for R
Output: decomposition of R into 4NF relations with “lossless join”
Compute keys for R
Repeat until all relations are in 4NF:
Pick any R’ with nontrivial A B that violates 4NF
Decompose R’ into R1(A, B) and R2(A, rest)
Compute FDs and MVDs for R1 and R2
Compute keys for R1 and R2

14. BCNF Decomposition Example #1
MVDs & 4NF
BCNF Decomposition Example #1
Apply(SSN, cName, hobby)

15. BCNF Decomposition Example #2
MVDs & 4NF
BCNF Decomposition Example #2
Apply(SSN, cName, date, major, hobby)

16. Relational design MVDs & 4NF
Functional dependencies & Boyce-Codd Normal Form
Multivalued dependences & Fourth Normal Form