1. Relational Database Design • Informal design guideline • First Normal Form • Functional Dependencies • Key • Normal form • Second normal form • Third Normal Form • Boyce-Codd Normal Form

2. Informal design guideline Design a relation schema so that • It is easy to explain its meaning • avoid redundant data • No update anomalies • Avoid null values • Relations can be joined without spurious tuples.

3. Design guideline : Clear meaning • Design a relation schema so that it is easy to explain its meaning. Do not combine attributes from multiple entity types and relationship types into a single relation. • Figure 14.4

4. Design guideline: Avoid redundant information • One of goal of schema design is to minimize the storage space that the base relations occupy. • Figure 14.4

5. Design guideline: no update anomalies • Insertion anomalies • Delete anomalies • Modification anomalies

6. Design guideline: avoid null values • Null value can: • Waste space • Will give a wrong results of aggregation operations • Null value can have multiple interpretations. • As far as possible, avoid placing attributes in a base relation whose values may frequently be null.

7. Generation of spurious tuples • Figure 14.5 • Figure 14.6

8. First Normal Form • Domain is atomic if its elements are considered to be indivisible units • Examples of non-atomic domains: • Set of names, composite attributes • A relational schema R is in first normal form if the domains of all attributes of R are atomic • We assume all relations are in first normal form. • Figure 14.8

9. Functional Dependencies • Constraints on the set of legal relations. • Require that the value for a certain set of attributes determines uniquely the value for another set of attributes. • A functional dependency is a generalization of the notion of a key.

10. FD definition • Let R be a relation schema X  R and Y  R • The functional dependency X  Yholds onR if and only if for any legal relations r(R), whenever any two tuples t1and t2 of r agree on the attributes , they also agree on the attributes . That is, t1[] = t2 []  t1[ ] = t2 [ ] • Example: Consider r(A,B) with the following instance of r. • On this instance, AB does NOT hold, but BA does hold. • 4 • 1 5 • 3 7

11. Use of Functional Dependencies (I) • We use functional dependencies to: • test relations to see if they are legal under a given set of functional dependencies. • If a relation r is legal under a set F of functional dependencies, we say that rsatisfies F.

12. Use of Functional Dependencies (I) • Functional dependencies allow us to express constraints that cannot be expressed using superkeys. Consider the schema: Loan-info-schema = (customer-name, loan-number, branch-name, amount). We expect this set of functional dependencies to hold: loan-numberamount loan-number  branch-name but would not expect the following to hold: loan-number customer-name

13. Use of Functional Dependencies (II) • Note: A specific instance of a relation schema may satisfy a functional dependency even if the functional dependency does not hold on all legal instances. • For example, a specific instance of Loan-schema may, by chance, satisfy loan-number customer-name.

14. Inference rules for Functional Dependencies • if X  Y, then Y X (reflexivity) • if X Y, then ZX  ZY(augmentation) • if X Y, and Y  Z, then X  Z(transitivity) • if X YZ , then X  Y (decomposition) • if X Y, and X  Y, then X  YZ (union)

15. Inference rules for Functional Dependencies • A functional dependency is trivial if it is satisfied by all instances of a relation • E.g. • customer-name, loan-number customer-name • customer-name customer-name • In general,   is trivial if   

16. Closure of Attribute Sets • Given a set of attributes a, define the closureof aunderF (denoted by a+) as the set of attributes that are functionally determined by a under F: • Algorithm to compute a+, the closure of a under F result := a;while (changes to result) do for each in F do begin if  result then result := result end

17. Example of Attribute Set Closure • R = (A, B, C, G, H, I) • F = {A BA C CG HCG IB H} • (AG)+ 1. result = AG 2. result = ABCG (A C and A  B) 3. result = ABCGH (CG H and CG  AGBC) 4. result = ABCGHI (CG I and CG  AGBCH)

18. Key • K is a superkey for relation schema R if and only if K R • K is a candidate key for R if and only if • K R, and • for no   K,  R

19. Key: find a key • R = (A, B, C, G, H, I) • F = {A BA C CG HCG IB H} • Is AG a candidate key? • Is AG a super key? • Does AG R? == Is (AG)+  R • Is any subset of AG a superkey? • Does AR? == Is (A)+  R • Does GR? == Is (G)+  R

20. Normal form: second normal form • Problem of first normal form • Figure 10.10

21. Second normal form • A relation schema R is in second normal form if evey non prime attribute A in R is not partially dependent on any key of R. • Formally: A relation schema R is in second normal form (2NF) if for all non trivial function dependent X A in F+ If A is not contained in any candidate key for R, and X is not a candidate key, then not exist any cnadidate key that contains X.

22. Third Normal Form • Problem of second normal form • A relation schema R is in third normal form (3NF) if for all: X A in F+at least one of the following holds: • X  Ais trivial (i.e., A X) • X is a superkey for R • A is contained in a candidate key for R.

23. Third Normal form (cont) • Example • R = (J, K, L)F = {JK L, L K} • Two candidate keys: JK and JL • R is in 3NF JK L JK is a superkeyL K K is contained in a candidate key • Banker-schema = (branch-name, customer-name, banker-name) banker-name  branch name branch name customer-name  banker-name

24. BC normal form • Some redundancy in thrid normal form. • Fig 10.12

25. BC normal form definition A relation schema R is in BCNF with respect to a set F of functional dependencies if for all functional dependencies in F+ of the form XY, where X R and Y R,at least one of the following holds: • X Yis trivial (i.e., Y X) • X is a superkey for R