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2 Introduction to Databases 2 Chapter Outline Informal Design Guidelines for Relational Databases Functional Dependencies (FDs) Definition, Inference Rules and Normal Forms Based on Primary Keys Normal Forms Based on Primary Keys  First Normal Form  Second Normal Form  Third Normal Form BCNF (Boyce-Codd Normal Form)

3 Introduction to Databases 3 Informal Design Guidelines for Relational Databases Relational database design: The grouping of attributes to form "good" relation schemas Two levels of relation schemas:  The logical "user view" level  The storage "base relation" level Design is concerned mainly with base relations Criteria for "good" base relations:  Discuss informal guidelines for good relational design  Discuss formal concepts of functional dependencies and normal forms 1NF 2NF 3NF BCNF

4 Introduction to Databases 4 Informal Design Guidelines for Relational Databases Four informal measures of quality for relation schema design: 1. Semantics of the Relation Attributes 2. Reducing the redundant information in tuples 3. Reducing Null values in tuples 4. Disallowing the possibility of one generating spurious tuples.

5 Introduction to Databases 5 1- Semantics of the Relation Attributes Each tuple in a relation should represent one entity or relationship instance  Only foreign keys should be used to refer to other entities  Entity and relationship attributes should be kept apart as much as possible Guideline #1: Design a schema that can be explained easily relation by relation. The semantics of attributes should be easy to interpret.

6 Introduction to Databases 6 2- Redundant Information in Tuples and Update Anomalies Mixing attributes of multiple entities may cause problems:  Information is stored redundantly wasting storage  Problems with update anomalies: Insertion anomalies Deletion anomalies Modification anomalies Attributes of different entities (EMPLOYEEs, DEPARTMENTs, PROJECTs) should not be mixed in the same relation.

7 Introduction to Databases 7 Example of An Update Anomaly Consider the relation: EMP_PROJ ( Emp#, Proj#, Ename, Pname, No_hours)  Update Anomaly Changing the name of project number P1 from “Billing” to “Customer-Accounting” may cause this update to be made for all 100 employees working on project P1  Insert Anomaly Cannot insert a project unless an employee is assigned to. Inversely- Cannot insert an employee unless he/she is assigned to a project.

8 Introduction to Databases 8  Delete Anomaly When a project is deleted, it will result in deleting all the employees who work on that project. Alternately, if an employee is the sole employee on a project, deleting that employee would result in deleting the corresponding project. Guideline #2: Design a schema that does not suffer from the insertion, deletion and update anomalies. If there are any present, then note them so that applications can be made to take them into account Example of An Update Anomaly (contd.)

9 Introduction to Databases 9 Two relation schemas suffering from update anomalies

10 Introduction to Databases 10 Base Relations EMP_PROJ formed after a Natural Join : with redundant information

11 Introduction to Databases 11 3- Null Values in Tuples Reasons for nulls: a. attribute not applicable or invalid b. attribute value unknown (may exist) c. value known to exist, but unavailable Guideline #3: Relations should be designed such that their tuples will have as few NULL values as possible Attributes that are NULL frequently could be placed in separate relations (with the primary key)

12 Introduction to Databases 12 4- Spurious Tuples Bad designs for a relational database may result in erroneous results for certain JOIN operations The "lossless join" property is used to guarantee meaningful results for join operations Guideline #4: The relations should be designed to satisfy the lossless join condition. No spurious tuples should be generated by doing a natural-join of any relations

13 Introduction to Databases 13 Functional Dependencies Functional dependencies (FDs) are used to specify formal measures of the "goodness" of relational designs FDs and keys are used to define normal forms for relations FDs are constraints that are derived from the meaning and interrelationships of the data attributes

14 Introduction to Databases 14 Functional Dependencies (2) A set of attributes X functionally determines a set of attributes Y if the value of X determines a unique value for Y X  Y holds if whenever two tuples have the same value for X, they must have the same value for Y If t1[X]=t2[X], then t1[Y]=t2[Y] in any relation instance r(R) X  Y in R specifies a constraint on all relation instances r(R) FDs are derived from the real-world constraints on the attributes Written as X -> Y; can be displayed graphically on a relation schema as in Figures. (denoted by the arrow ).

15 Introduction to Databases 15 Examples of FD constraints Social security number determines employee name SSN -> ENAME Project number determines project name and location PNUMBER -> {PNAME, PLOCATION} Employee ssn and project number determines the hours per week that the employee works on the project {SSN, PNUMBER} -> HOURS If K is a key of R, then K functionally determines all attributes in R (since we never have two distinct tuples with t1[K]=t2[K])

16 Introduction to Databases 16 Introduction to Normalization Normalization: Process of decomposing unsatisfactory "bad" relations by breaking up their attributes into smaller relations Normal form: Condition using keys and FDs of a relation to certify whether a relation schema is in a particular normal form  2NF, 3NF, BCNF based on keys and FDs of a relation schema  4NF based on keys, multi-valued dependencies

17 Introduction to Databases 17 First Normal Form Disallows composite attributes, multivalued attributes, and nested relations; attributes whose values for an individual tuple are non-atomic. Considered to be part of the definition of relation

18 Introduction to Databases 18 Normalization into 1NF

19 Introduction to Databases 19 Examples First Normal Form EMP_PROJ (Ssn, Ename, {Phone#}) { } Mulitvalue attribute EMP_PROJ1 (Ssn, Ename) EMP_PROJ2 (Ssn, Phone#) ■EMP_PROJ (Ssn, Ename (Fname, Lname)) ( ) composite attribute EMP_PROJ (Ssn, Fname,Lname) ■EMP_PROJ (Ssn, Ename, {PROJS (Pnamber, Hours)}) EMP_PROJ1 (Ssn, Ename) EMP_PROJ2 (Ssn, Pnamber, Hours)

20 Introduction to Databases 20

21 Introduction to Databases 21 Second Normal Form Uses the concepts of FDs, primary key Definitions:  Prime attribute - attribute that is member of the primary key K  Full functional dependency - a FD Y  Z where removal of any attribute from Y means the FD does not hold any more

22 Introduction to Databases 22 Examples Second Normal Form {SSN, PNUMBER}  HOURS is a full FD since neither SSN  HOURS nor PNUMBER  HOURS hold {SSN, PNUMBER}  ENAME is not a full FD (it is called a partial dependency ) since SSN  ENAME also holds A relation schema R is in second normal form (2NF) if every non-prime attribute A in R is fully functionally dependent on the primary key R can be decomposed into 2NF relations via the process of 2NF normalization

23 Introduction to Databases 23 Examples Second Normal Form

24 Introduction to Databases 24 Second Normal Form Note: The test for 2NF involves testing for functional dependencies whose left-hand side attributes are part of the primary key. If the primary key contains a single attribute, the test need not be applied at all.

25 Introduction to Databases 25 Third Normal Form Definition  Transitive functional dependency – a FD X  Y in R is a transitive dependency if there is a set of attributes Z that are neither a primary or candidate key and both X  Z and Z  Y holds. Examples:  SSN  DMGRSSN is a transitive FD since SSN  DNUMBER and DNUMBER  DMGRSSN hold  SSN  ENAME is non-transitive since there is no set of attributes X where SSN  X and X  ENAME

26 Introduction to Databases 26 3 rd Normal Form A relation schema R is in third normal form (3NF) if it is in 2NF and no non-prime attribute A in R is transitively dependent on the primary key

27 Introduction to Databases 27 Third Normal Form (2) NOTE:  In X -> Y and Y -> Z, with X as the primary key, we consider this a problem only if Y is not a candidate key.  When Y is a candidate key, there is no problem with the transitive dependency.  E.g., Consider EMP (SSN, Emp#, Salary ). Here, SSN -> Emp# -> Salary and Emp# is a candidate key.

28 Introduction to Databases 28 Examples Third Normal Form

29 Introduction to Databases 29 BCNF (Boyce-Codd Normal Form) A relation schema R is in Boyce-Codd Normal Form (BCNF) if whenever an FD X  A holds in R, then X is a superkey of R  Each normal form is strictly stronger than the previous one: Every 2NF relation is in 1NF Every 3NF relation is in 2NF Every BCNF relation is in 3NF  There exist relations that are in 3NF but not in BCNF  The goal is to have each relation in BCNF (or 3NF)

30 Introduction to Databases 30 BCNF R1(A,C) R2(C,B)

31 Introduction to Databases 31

32 Introduction to Databases 32 BCNF FDs: {Student,course}  Instructor Instructor  Course It is in 3NF not in BCNF Decomposing into 2 schemas {Student, Instructor} {Instructor, Course}

33 Introduction to Databases 33 Examples BCNF R ( Client#, Problem, Consultant _name) R1 (Client#, Consultant _name) R2 (Consultant _name, Problem) ■R (Stud#, Class#, Instructor, Grade) R1 (Stud#, Instructor, Grade) R2 (Instructor, Class#)

34 Introduction to Databases 34 Example Consider the following relation for published books: BOOK (Book_title, Author_name, Book_type, Listprice, Author_affil, Publisher) - Author_affil referes to the affiliation of the author. Suppose thefollowing dependencies exist: Book_title -> Publisher, Book_type Book_type -> Listprice Author_name -> Author-affil (a) What normal form is the relation in? Explain your answer. (b) Apply normalization until you cannot decompose the relations further. State the reasons behind each decomposition.

35 Introduction to Databases 35 Answer BOOK (Book_title, Authorname, Book_type, Listprice, Author_affil, Publisher) (a) The key for this relation is (Book_title, Authorname). This relation is in 1NF and not in 2NF as no attributes are FFD on the key. It is also not in 3NF. (b) 2NF decomposition: Book0(Book_title, Authorname) Book1(Book_title, Publisher, Book_type, Listprice) Book2(Authorname, Author_affil) This decomposition eliminates the partial dependencies. 3NF decomposition: Book0(Book_title, Authorname) Book1-1(Book_title, Publisher, Book_type) Book1-2(Book_type, Listprice) Book2(Authorname, Author_affil) This decomposition eliminates the transitive dependency of Listprice

36 Introduction to Databases 36 Example Given the relation schema Car_Sale (Car#, Salesman#, Date_sold, Commission%, Discount_amt) with the functional dependencies Date_sold -> Discount_amt Salesman# -> Commission% Car# -> Date_sold This relation satisfies 1NF but not 2NF (Car# -> Date_sold and Salesman# -> Commission%) so these two attributes are not FFD on the primary key and not 3NF

37 Introduction to Databases 37 To normalize, 2NF: Car_Sale1 (Car#, Salesman#) Car_Sale2 (Car#, Date_sold, Discount_amt) Car_Sale3 (Salesman#,Commission%) 3NF: Car_Sale1(Car#, Salesman#) Car_Sale2-1(Car#, Date_sold) Car_Sale2-2(Date_sold, Discount_amt) Car_Sale3(Salesman#,Commission%) Answer

38 Introduction to Databases 38 SUMMARY OF NORMAL FORMS based on Primary Keys


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