1. NormalizationNormalization Chapter 4

3. Purpose of Normalization Normalization  A technique for producing a set of relations with desirable properties, given the data requirements of an enterprise.  The process of normalization is a formal method that identifies relations based on their primary or candidate keys and on the functional dependencies among their attributes.  Normalization supports a number of tests, which can be applied to relations so that a relational schema can be normalized to a specific form to prevent the possible occurrence of update anomalies.

4. First Normal Form Relation We saw before that a relation should have the following properties: A relation in a database has a unique name. Each cell of the relation contains exactly one atomic value. Each attribute has a distinct name within a relation. The values of an attribute are all from the same domain. The order of the attributes has no significance. Each tuple is distinct; there are no duplicate tuples. The order of tuples has no significance, theoretically. In that case we say that the relation is in FIRST NORMAL FORM (1NF).

5. Normalization Process: 1NF Un-normalized form  A table that contains repeating Groups First Normal Form  A relation in which the inter- section of each row and column contains one and only one value

6. Sample Database : 1NF Constraints Primary Key : S#, P# A city has a specific status A Supplier Is located in one City First

7. Update Anomalies Insertion Anomalies  each time we insert a new part for a supplier we have to repeat status and city  we cannot insert a new supplier before he supplies a part Deletion Anomaly  If we delete the fact that S3 supplies P2 we delete the row and we do not know anymore that he is located in Paris Modification Anomalies  If S1 moves from London to Berlin we have to modify 6 rows  If the status of London changes we have to modify 9 rows in order to avoid inconsistency

8. Functional Dependencies Functional Dependency  Describes the relationship between attributes in a relation  If A and B are attributes of relation R, B is functionally dependent on A, if each value of A in R is associated with exactly one value of B in R  notation A  B  Functional dependency diagram Determinant  The determinant of a functional dependency refers to the attribute or group of attributes on the starting point of the arrow AB B is functionally dependent on A

9. Functional Dependencies in FIRST QTY S# P# Status City

10. Sample Database : 1NF Constraints Primary Key : S#, P# A city has a specific status A Supplier Is located in one City First

11. Lossless-join and Dependency Preservation Properties Two important properties of decomposition  Lossless-join property enables us to find any instance of the original relation from corresponding instances in the smaller relations.  Dependency preservation property enables us to enforce a constraint on the original relation by enforcing some constraint on each of the smaller relations.

12. Full Functional Dependency Full Functional Dependency indicates that if A and B are attributes of a relation, B is fully functionally dependent on A if B is functionally dependent on A, but not on a proper subset of A. e.g.First.(S#, Status ) First.City First. S#First.City In fact full functional dependence is a more important concept than functional dependence

13. Normalization Process: 2NF A relation is in second normal form if it is in first normal form and every non-primary-key attribute is fully functional dependent on the primary key. The reduction consists of a suitable projection Supplier 5 is inserted If in a 1NF relation the primary has only one attribute, the relation is also in 2NF SPSecond

14. Functional Dependencies in SP and Second QTY S# P# Status City S# Elimination of non-fully functional dependencies

15. Normalization Process: 3NF A relation in third normal form is a relation that is in first and second normal form, and in which no non- primary-key attribute is transitively dependent on the primary key. SCCS

16. Functional Dependencies in SP, SC and CS QTY S# P# City S# Status Elimination of transitive dependencies

17. Inter-relational Dependency QTY S# P# City S# Status The three relations are also in 3NF but there is an inter-relational dependency Bad decomposition

18. Normalization Process: BCNF A relation is in Boyce-Codd normal form if and only if every determinant is a candidate key.  This definition doesn’t refers to other normal forms.  BCNF is stronger than 3NF If a relation is in third normal form, violation of the BCNF is quite rare. It may only happen under the specific conditions that the relation :  contains two or more composite candidate keys  which overlap and share at least one attribute in common  this attribute is fully dependent on the primary key

19. Boyce-Codd Normal Form (BCNF) Violation of BCNF may occur in a relation that  contains two (or more) composite keys  which overlap and share at least one attribute in common.

20. Multivalued Dependency In R(A,B,C) the multivalued dependency R.A R.B holds in R, if and only if the set of B-values matching a given pair (A,C) is independent of the C-value.  Multivalued dependencies always go together in pairs  notation R.A R.B R.C  functional dependency is a special case of multivalued dependency  example CTX

21. Normalization Process: 4NF CTX Normalized 4NF CTX.Course CTX.Teacher CTX.Course CTX.Text Omit multivalued dependencies