Multivalued dependency
- 1. Multivalued Dependency Tamer Abuelata
- 2. Introduction Goal in Databases: BCNF (Boyce Codd Normal Form) Losslessness Dependency preservation
- 3. Remember… Boyce Codd Normal Form (BCNF) eliminates all redundancy that can be discovered based on functional dependencies.
- 4. Issue Some relation schemas, even though they are in BCNF, do not seem to be sufficiently normalized. They still contain repetitions
- 5. Case study Consider the bank database schema: cust_loan = ( loan_number, cust_id , cust_name, cust_street, cust_city) This is BCNF because of the functional dependency: cust_id -> cust_name, cust_street cust_city And because cust_id is not a key for cust_loan
- 6. Case Study But what if some customers have several addresses? We no longer wish to enforce the func. dependency: cust_id ->cust_street cust_city But we still want to enforce cust_id -> cust_name
- 7. Case Study Following BCNF decomposition algorithm we get: R1 = ( cust_id , cust_name) R2 = ( loan_number, cust_id , cust_street, cust_city) (both in BCNF)
- 8. Case Study The issue Despite R2 in BCNF, there is redundancy. We repeat the address of each residence for each loan that the customer has.
- 9. Case Study We can therefore decompose further into: loan_cust_id = (loan_number, cust_id) cust_residence = (cust_id, cust_street, cust_city) But there is no constraint that lead us to do that. To deal with this, we need a few form of constraint: 4NF.
- 10. 4NF We can use multivalued dependencies to define the fourth normal form
- 11. 4NF A relation schema R is in fourth normal form with respect to a set D of functional and multivalued dependencies if, for all multivlued dependencies in D+ of the form A -->-> B at least one of the following holds: A -->-> B is a trivial multivalued dependency A is a superkey for schema R
- 12. Multivalued Dependency Requires that other tuples of a certain form be present in the relation. Multivalued Dependencies The multivalued dependency relates to this problem when more than one multivalued attributes exist. Also referred to as: tuple-generating dependency
- 13. Example R relation schema, A and B follow the multivalued dependency : A -->-> B The relationship between A and B is independent of the relation between A and R – B If A -->-> B is satisfied by all relations on R then A -->-> B is a trivial multivalued dependency
- 14. Example Let’s reconsider R2 = ( loan_number, cust_id , cust_street, cust_city) loan_number cust_id cust_street cust_city L-23 99-123 North Rye L-23 99-123 Main Manchester L-93 15-106 Lake Horseneck
- 15. Example We must repeat the loan number once for each address a customer has and we must repeat the address for each loan a customer has. loan_number cust_id cust_street cust_city L-23 99-123 North Rye L-23 99-123 Main Manchester L-93 15-106 Lake Horseneck
- 16. Example We must repeat the loan number once for each address a customer has and we must repeat the address for each loan a customer has. This repetition is unnecessary since the relationship between a customer and his address is independent of the relationship between that customer and a loan. loan_number cust_id cust_street cust_city L-23 99-123 North Rye L-23 99-123 Main Manchester L-93 15-106 Lake Horseneck
- 17. Example Therefore this relation is illegal loan_number cust_id cust_street cust_city L-23 99-123 North Rye L-27 99-123 Main Manchester
- 18. Example Therefore this relation is illegal To make it legal we should add tuples (L23, 99-123, Main, Manchester) and (L27, 99-123, North, Rye) loan_number cust_id cust_street cust_city L-23 99-123 North Rye L-27 99-123 Main Manchester
- 19. Example Updated table (legal) loan_number cust_id cust_street cust_city L-23 99-123 North Rye L-27 99-123 Main Manchester L-23 99-123 Main Manchester L-27 99-123 North Rye
- 20. Example Updated table (legal) We want Cust_id -->-> cust_street cust_city to hold loan_number cust_id cust_street cust_city L-23 99-123 North Rye L-27 99-123 Main Manchester L-23 99-123 Main Manchester L-27 99-123 North Rye
- 21. Conclusion We can use multivalued dependencies To test relations to determine whether they are legal under a given set of functional and multivalued dependencies To specify constraints on the set of legal relations