Lecture 3 (Part 2) Akhtar Ali

Transcription

1 Normalisation Lecture 3 (Part 2) Akhtar Ali 10/14/2014 1

2 Learning Objectives 1. To consider the process of Normalisation 2. To consider the definition and application of 1NF 3. To consider the definition and application of 2NF 4. To consider the definition and application of 3NF 10/14/2014 2

3 NORMALISATION PRINCIPLES 10/14/2014 3

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. 10/14/2014 4

5 How Normalization Supports Database Design? 10/14/2014 5

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. 1NF 2NF 3NF 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. 10/14/2014 6

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 a 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. 10/14/2014 7

8 The Normalisation Procedure The normalisation procedure starts with a set of relations, for each of which, it is presumed to be unnormalised 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, so do nothing ELSE create 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. 8

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. 10/14/2014 9

10 Normalising : Possibilities The set of all un-normalised relations The set of all relations in 1NF The set of all relations in 2NF A given relation. Already in 1NF. Nothing to do. Relation Already in 2NF. Nothing to do. And so on. 10/14/

11 Consequences of Normalisation If new, replacement relations are created, then they must be projections of the original. New-Relation π set of attributes (Original-relation) The symbol π denotes projection of a set of attributes from a relation. Normalisation always creates new 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. 10/14/

12 FIRST NORMAL FORM (1NF) 10/14/

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. 10/14/

14 Example : Purchase Order Relation The following relation holds data about purchase orders placed on suppliers for parts Ord Sno Sname Saddr Date Part Pname Qty Price Tot L5 127 Smith N cle 7 May N8 B6 L4 Nut Bolt Nail L6 315 Bloggs D ham 8 June P3 Q7 Pump Motor Ord Sno Sname Saddr Date Part Pname Qty Price Tot Order number that uniquely identifies every purchase order. Supplier number that uniquely identifies any supplier. The name of a supplier. The address of a supplier. The date on which the order was placed. Part number that uniquely identifies every kind of part used by the company. The name of a particular kind of part. The quantity of a particular kind of part ordered on a purchase order. The price of that quantity of that particular kind of part. The total price to be paid for the whole order. 10/14/

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. 10/14/

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. Ord Sno Sname Saddr Date Tot L5 127 Smith N cle 7 May 12 L6 315 Bloggs D ham 8 June /14/

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. 10/14/

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. Part Pname Qty Price N8 Nut 70 4 B6 Bolt 60 5 L4 Nail P3 Pump Q7 Motor /14/

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. Ord Part Pname Qty Price L5 N8 Nut 70 4 L5 B6 Bolt 60 5 L5 L4 Nail L6 P3 Pump L6 Q7 Motor /14/

20 Candidate Keys for Relations The candidate key is Ord Ord Sno Sname Saddr Date Tot L5 127 Smith N cle 7 May 12 L6 315 Bloggs D ham 8 June 400 Extend the candidate key to Ord and Part including the foreign key Ord* Ord* Part Pname Qty Price L5 N8 Nut 70 4 L5 B6 Bolt 60 5 L5 L4 Nail L6 P3 Pump L6 Q7 Motor /14/

21 SECOND NORMAL FORM (2NF) 10/14/

22 Definition of 2NF A relation is in 2NF if and only if it is in 1NF and every non-key attribute is fully functionally dependent on the candidate key. The extra constraint applied by 2NF Note that 2NF is more strict than 1NF because it requires the relation to conform to the additional full functional dependency constraint. 10/14/

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. 10/14/

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. Account Number Payment Due This type of arrow indicates a function dependency. 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). 10/14/

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. 10/14/

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. 10/14/

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. 10/14/

28 Further FD Examples Example 1: Supplier Name Supplier Number Supplier Address Supplier Telephone No. A set containing one attribute determining a set of three attributes. Example 2: a set of two attributes determining a set containing one attribute. Customer Name Customer Address Customer Telephone No. 10/14/

29 Full Functional Dependency & 2NF The definition of 2NF requires not merely functional dependency, but full functional dependency. 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. 10/14/

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. 10/14/

31 Examples: Purchase Order Relations P_ORDER_1: FD Diagram The functional dependencies of the non-key attributes in P_ORDER_1 on its candidate key can be represented by the following FD diagram :- P_ORDER_1 Ord Sno Sname Saddr Date Tot L5 127 Smith N cle 7 May 12 L6 315 Bloggs D ham 8 June 400 Sno As they are all fully FD on Ord, the relation is already in 2NF. Sname Ord Saddr Date 10/14/ Tot

32 P-ITEM-1: FD Diagram P-ITEM-1 Ord* Part Pname Qty Price L5 N8 Nut 70 4 L5 B6 Bolt 60 5 L5 L4 Nail L6 P3 Pump L6 Q7 Motor /14/

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. 10/14/

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. 10/14/

35 Redundant Data Every time a part type appears on an order (say Q7), its name (Motor) also appears. N.B. The part number (say Q7) is enough to identify the part type. P-ITEM-1 Ord* Part Pname Qty Price L5 N8 Nut 70 4 L5 B6 Bolt 60 5 L5 L4 Nail L6 P3 Pump L6 Q7 Motor L7 Q7 Motor Example: Pname is unnecessarily repeated. Motor is repeated in orders L6 & L7. One order is sufficient to give us the name, so the Pname is redundant (either one). 10/14/

36 Update Anomalies Example: Part type details (Part and Pname) cannot always be updated. P-ITEM-1 Ord* Part Pname Qty Price L5 N8 Nut 70 4 L5 B6 Bolt 60 5 L5 L4 Nail L6 P3 Pump L6 Q7 Motor L7 Q7 Engine 2 100?? F5 Flange??? 10/14/

37 Semantic Problems P-ITEM-1 Ord* Part Pname Qty Price L5 N8 Nut 70 4 L5 B6 Bolt 60 5 L5 L4 Nail L6 P3 Pump L6 Q7 Motor L7 Q7 Engine Q7 now has two different names. 10/14/

38 Putting P_ITEM_1 into 2NF (1) Price The problem is caused by Pname being FD on just part, not the whole of the candidate key. Ord Part Qty Pname The solution is to separate out each determinant and its dependents. Create 2 replacement relations based on these FDs. Ord Part Price Qty Part Pname 10/14/

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. 10/14/

40 Putting P_ITEM_1 into 2NF (2) P-ITEM-2 Ord* Part Qty Price L5 N L5 B L5 L L6 P L6 Q L7 Q /14/

41 Putting P_ITEM_1 into 2NF (3) PART_2 Part N8 B6 L4 P3 Q7 Pname Nut Bolt Nail Pump Motor 10/14/

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 10/14/

43 THIRD NORMAL FORM (3NF) 10/14/

44 Definition of 3NF A relation is in 3NF if and only if it is in 2NF and every non-key attribute is non-transitively fully FD on the candidate key. The extra constraint applied by 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. 10/14/

45 Transitivity Assume there are three sets of attributes, A, B and C. Let and A B B C These FDs are non-transitive i.e. direct, because they do not go via any other sets of attributes. If A determines B, and B determines C, then logically A determines C, but transitively via B. Then A C This FD is transitive, because it is via another set of attributes, in this case B. 10/14/

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. 10/14/

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. 10/14/

48 Reviewing the Definition of 3NF 1. R1 s FD diagram shows a chain of dependencies. It is not in 3NF. R1( Key, NK1, NK2, NK3 ) Key NK1 NK2 NK3 2. R2( Key, NK1, NK2, NK3 ) R2 s FD diagram shows no chain of dependencies. It is in 3NF. Key NK1 NK2 10/14/ NK3

49 Example: P_ITEM_2 P-ITEM-2 Ord* Part Qty Price L5 N L5 B L5 L L6 P L6 Q L7 Q Neither Price nor Qty is FD on the candidate key via the other, but nontransitively FD on the key. Thus P_ITEM_2 is already in 3NF. 10/14/

50 Example : PART_2 PART_2 Part N8 B6 L4 P3 Q7 Pname Nut Bolt Nail Pump Motor 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. 10/14/

51 Example : P_ORDER_1 P_ORDER_1 Ord Sno Sname Saddr Date Tot L5 127 Smith N cle 7 May 12 L6 315 Bloggs D ham 8 June 400 Sno Sname As we have already seen, its FD diagram is :- Ord Saddr However, not all of these FDs are nontransitive FDs (= NTFDs). Date Tot Sname Taking account now of transitivity, the FD diagram can be re-drawn as:- Ord Hence P_ORDER_1 is not in 3NF. 10/14/ Sno Date Tot Saddr

52 Putting P_ORDER_1 into 3NF (1) The problem is caused by Sname and Saddr being only transitively FD on the candidate key. Ord Sno Date Sname Saddr Tot Solution: separate out each determinant and its NTFD dependents, & create 2 replacement relations based on them. Sno Sname Ord Date Sno Saddr Tot 10/14/

53 Putting P_ORDER_1 into 3NF (2) Sno Ord Date Tot P_ORDER_3 Ord Sno Date Tot The corresponding relation is:- L May 12 L June /14/

54 Putting P_ORDER_1 into 3NF (3) Sname Sno Saddr SUPPLIER_3 Sno Sname Saddr The corresponding relation is:- 127 Smith N cle 315 Bloggs D ham 10/14/

55 Benefits No information has been lost. A natural join of P_ORDER_3 and SUPPLIER_3 on attribute Sno will re-create the original relation P_ORDER_1. Problems Solved: Redundant data removed each Sname in once Update anomalies no side effects in operations Semantic problems each supplier has just one name 10/14/