Normalisation

1. Normalisation Lecture 3 (Part 2) Akhtar Ali

2. Learning Objectives • To consider the process of Normalisation • To consider the definition and application of 1NF • To consider the definition and application of 2NF • To consider the definition and application of 3NF

3. NORMALISATION PRINCIPLES

4. Normalisation • Definition : a systematic method that takes pre-existing relations and produces a canonical set of relations. • By canonical is meant well-designed, sound, or a recognised and lawful form. • It can be used both for : • designing canonical relations, • checking existing relations to ensure they are canonical.

5. How Normalization Supports Database Design?

6. Normal forms Normalisation uses the concept of Normal Forms. They are organised in a sequence, each successive normal form being higher than the one before. A normal form is higher because it applies more stringent constraints to a relation than a lower normal form. A relation is said to a be in a certain “normal form” if it conforms to the constraints of that normal form.

7. Normalisation as a Relational Design Tool • Sometimes, we need to use normalisation for designing relations. • For example, when ER modelling is not feasible or if we deal with small number of attributes. • So we need to learn normalisation. • 1NF stands for First Normal Form, 2NF for Second Normal Form, and so on. • The constraints of a particular normal form are those of the previous normal form • plus the additional constraint(s) peculiar to this particular normal form.

8. The Normalisation Procedure • The normalisation procedure starts with a set of relations, each of which, it is presumed, may be un-normalised or in 0NF. • DO FOR xNF = 1NF, ..... 5NF • DO FOR each relation that exists • IF relation already conforms to xNF • THEN it is in xNF, sodo nothing • ELSEcreate 2 or more replacement relations from it that do conform to xNF. • END-LOOP • END-LOOP • 5NF is the highest possible normal form. •  In practice, 3NF is the highest normal form usually reached.

9. What is a Normal Form? • Each Normal Form has two parts • A definition that specifies exactly what constraints apply to a relation in that normal form. • This is used to check whether any given relation is already in that normal form or not. • A method to be used to replace the relation with 2 or more that will be in that normal form. • The method assumes that the relation-to-be-replaced is in the previous normal form.

10. Normalising : Possibilities

11. Consequences of Normalisation • If new, replacement relations are created, then they must be projections of the original. • New-Relation πset of attributes(Original-relation) • The symbol πdenotes projection of a set of attributes from a relation. • Normalisation always createsnew relations such that • Original-relation New-Rel-1 ⋈New-Rel-2 • The symbol ⋈denotes a join between two relations. • This ensures that no information is ever lost.

12. First Normal form (1NF)

13. Definition of 1NF • A relation is in 1NF if and only if every attribute value it can ever contain is an atomic value • Question : What is an atomic value ? • Answer : A value that cannot meaningfully be broken down into two or more constituent parts.

14. Example : Purchase Order Relation The following relation holds data about purchase orders placed on suppliers for parts Ord Order number that uniquely identifies every purchase order. Sno Supplier number that uniquely identifies any supplier. Sname The name of a supplier. Saddr The address of a supplier. Date The date on which the order was placed. Part Part number that uniquely identifies every kind of part used by the company. Pname The name of a particular kind of part. Qty The quantity of a particular kind of part ordered on a purchase order. Price The price of that quantity of that particular kind of part. Tot The total price to be paid for the whole order.

15. Not in 1NF • Attributes Ord, Sno, Sname, Saddr, Date and Tot currently contain only atomic values, and in fact can only ever contain atomic values. • Attributes Part, Pname, Qty and Price currently contain non-atomic values, and in fact may often contain non-atomic values. • Therefore the relation is not in 1NF.

16. Putting Purchase Order into 1NF Separate out the atomic and non-atomic attributes Put all the atomic attributes in a new replacement relation, which then by definition is in 1NF.

17. The Non-Atomic Attributes • We can’t just throw away this data because it is a nuisance to store! • The values in all these attributes repeat together. • If a part is removed from an order, its values must be removed from all 4 attributes. • If another part is placed on an order, there must be a value for that part in all 4 attributes.

18. Repeating Together • Thus a set of values that repeat together should become a tuple in a new relation. • Now the attributes in these tuples contain only atomic data ! • Thus we form another new replacement relation to hold the tuples of data that repeat together. • There is no intrinsic reason why all the non-atomic attributes in an un-normalised relation should always repeat together.

19. Foreign Keys • The problem with this relation is that the part data is no longer associated with its order data. • We no longer know which part type was ordered on which purchase order. • We can solve this problem by adding the (purchase) order number attribute to this relation. • In general, we must add the attribute(s) which formed a candidate key in the original relation, to this relation as a foreign key. This retains the relationship information.

20. Candidate Keys for Relations The candidate key is Ord Extend the candidate key to Ord and Part including the foreign key Ord*

21. Second normal form (2NF)

22. Definition of 2NF Note that 2NF is more strict than 1NF because it requires the relation to conform to the additional “full functional dependency” constraint.

23. Fully Functionally Dependent • Question : What does fully functionally dependent mean? • We will first consider the principle of functional dependency, and then see • what full functional dependency means, • the application to achieve 2NF.

24. Example of Functional Dependency Assume some kind of loan account where payments of a certain amount have to be made on a regular basis to pay off the loan. This means : • A given account number determines what payment is due. • In principle, given an account number, one can find out what regular payment is due. (May not always be easy or feasible in practice).

25. Terminology • The Account Number is said to functionally determine the Payment Due. • The Payment Due is said to be functionally dependent on the Account Number. • Both are equally good means of expression, and convenience and emphasis usually determine which of the two is preferred in any particular situation.

26. Definition of Functional Dependency (FD) A set of attributes Y in a relation is functionally dependent on a set of attributes X in the same relation if and only if a given set of attribute values in X determines a specific set of attribute values in Y for every instant of time.

27. Relationship X:Y in FD is many:1 • For any given set of values X, there is just one corresponding set of values Y. • It is possible that there may be many sets of values X for which there is just one set of values Y. • A functional dependency is a permanent association between attributes.

28. Further FD Examples A set containing one attribute determining a set of three attributes. a set of two attributes determining a set containing one attribute.

29. Full Functional Dependency & 2NF Definition of FULL Functional Dependency: A set of attributes Y is fully functionally dependent on a set of attributes X if and only if Y is functionally dependent on all the attributes of X and not just a subset of them. The definition of 2NF requires not merely functional dependency, but full functional dependency.

30. Condition for 2NF Thus, to be in 2NF means that: all attributes not in the candidate key are fully FD on all those attributes that are in the candidate key.

31. Examples: Purchase Order Relations P_ORDER_1: FD Diagram

32. P-ITEM-1: FD Diagram P-ITEM-1

33. Reason for non-2NF • Attributes Price and Qty depend on the full key. • They depend not only on what kind of part they refer to, but also on the order itself • the quantity of a part type ordered will vary with & depend on the order, as will the price since it depends on the quantity.  • However Pname depends solely on the type of part. • A particular kind of part will have the same name on every order on which it appears.

34. Three Problems of a Non-2NF Relation • Redundant data may be stored. • Update anomalies • there can be problems in inserting, deleting and amending some of the data. • Semantic problems. • relation does not reflect the real-world meaning of the data, leading to problems in its use.

35. Redundant Data Example: Pname is unnecessarily repeated.

36. Update Anomalies Example: Part type details (Part and Pname) cannot always be updated.

37. Semantic Problems

38. Putting P_ITEM_1 into 2NF (1)

39. Satisfaction of 2NF • A relation created with a determinant as its candidate key, and with non-key attributes that are fully functionally dependent on that candidate key, must be in 2NF by definition. • Note that a determining attribute - Part in the above example - can appear in more than one complete determinant. • This is perfectly acceptable. It just depends what attributes form determinants.

40. Putting P_ITEM_1 into 2NF (2)

41. Putting P_ITEM_1 into 2NF (3)

42. Benefits of 2NF • No information has been lost. • A natural join of P_ITEM_2 and PART_2 on attribute Part will re-create the original relation P_ITEM_1. • Problems Solved: • Redundant data removed – each Pname in once • Update anomalies – no side effects in operations • Semantic problems – each part type has just one name

43. Third Normal Form (3NF)

44. Definition of 3NF Question : What does non-transitively mean ? Note that 3NF is more stringent than 2NF, as it requires that the relation not only have full functional dependencies on the candidate key, but that these dependencies must now additionally be “non-transitive”.

45. Transitivity Assume there are three sets of attributes, ‘A’, ‘B’ and ‘C’. If A determines B, and B determines C, then logically A determines C, but transitively via B.

46. Example of Transitive FD • Suppose pilots always fly the same aircraft • then if we know the pilot, we know the aircraft; so pilot functionally determines aircraft. • If we know the aircraft, then we know the airline that owns it • so aircraft functionally determines airline. • Putting these two dependencies together • then pilot functionally determines airline. •  But the functional dependency of airline on pilot is transitive, because it goes via aircraft.

47. Non-Transitive Full FD & 3NF So, to be in 3NF means that  all attributes not in the candidate key are non-transitively - i.e. directly - fully FD on all those attributes that are in candidate key, and not FD on the candidate key via some other non-key attribute.

48. Reviewing the Definition of 3NF R1’s FD diagram shows a “chain of dependencies”. It is not in 3NF. R2’s FD diagram shows no “chain of dependencies”. It is in 3NF.

49. Example: P_ITEM_2 Neither ‘Price’ nor ‘Qty’ is FD on the candidate key via the other, but non-transitively FD on the key. Thus P_ITEM_2 is already in 3NF.

50. Example : PART_2 Thus PART_2 is already in 3NF. If a 2NF relation only has one non-key attribute, then it must already be in 3NF, as there is no other non-key attribute via which a transitive dependency can occur.