1. E/R Diagrams and Functional Dependencies

2. Modeling Subclasses The world is inherently hierarchical. Some entities are special cases of others We need a notion of subclass. This is supported naturally in object-oriented formalisms. Products Software products Educational products

3. Product namecategory price isa Educational ProductSoftware Product Age Groupplatforms Subclasses in E/R Diagrams

4. Understanding Subclasses Think in terms of records: –Product –SoftwareProduct –EducationalProduct field1 field2 field1 field2 field1 field2 field3 field4 field5

5. Subclasses to Relations Product namecategory price isa Educational ProductSoftware Product Age Groupplatforms NamePriceCategory Gizmo99gadget Camera49photo Toy39gadget Nameplatforms Gizmounix NameAge Group Gizmotodler Toyretired Product Sw.Product Ed.Product

6. Modeling Union Types with Subclasses FurniturePiece Person Company Say: each piece of furniture is owned either by a person, or by a company

7. Modeling Union Types with Subclasses Say: each piece of furniture is owned either by a person, or by a company Solution 1. Acceptable, imperfect FurniturePiecePerson Company ownedByPersonownedByCompany (What’s wrong ?)

8. Modeling Union Types with Subclasses Solution 2: better isa FurniturePiece Person Company ownedBy Owner isa

9. Constraints in E/R Diagrams Finding constraints is part of the modeling process. Commonly used constraints: Keys: social security number uniquely identifies a person. Single-value constraints: a person can have only one father. Referential integrity constraints: if you work for a company, it must exist in the database. Other constraints: peoples’ ages are between 0 and 150.

10. Keys in E/R Diagrams address namessn Person Product namecategory price No formal way to specify multiple keys in E/R diagrams Underline:

11. Single Value Constraints makes v. s.

12. Referential Integrity Constraints CompanyProduct makes CompanyProduct makes

13. Other Constraints CompanyProduct makes <100 What does this mean ?

14. Weak Entity Sets Entity sets are weak when their key comes from other classes to which they are related. UniversityTeam affiliation numbersportname

15. Handling Weak Entity Sets UniversityTeam affiliation numbersportname Convert to a relational schema (in class)

16. The Relational Data Model Data Modeling Data Modeling Relational Schema Relational Schema Physical storage Physical storage E/R diagrams Tables: column names: attributes rows: tuples Complex file organization and index structures.

17. Recalling The Terminology Name Price Category Manufacturer gizmo $19.99 gadgets GizmoWorks Power gizmo $29.99 gadgets GizmoWorks SingleTouch $149.99 photography Canon MultiTouch $203.99 household Hitachi Tuples or rows or records Attribute names Table name or relation name Products:

18. First Normal Form (1NF) A database schema is in First Normal Form if all tables are flat NameGPACourses Alice3.8 Bob3.7 Carol3.9 Math DB OS DB OS Math OS Student NameGPA Alice3.8 Bob3.7 Carol3.9 Student Course Math DB OS StudentCourse AliceMath CarolMath AliceDB BobDB AliceOS CarolOS Takes Course

19. Functional Dependencies A form of constraint –hence, part of the schema Finding them is part of the database design Also used in normalizing the relations

20. Functional Dependencies Definition: If two tuples agree on the attributes A, A, … A 12n then they must also agree on the attributes B, B, … B 12m Formally: A, A, … A 12n B, B, … B 12m

21. Examples EmpID Name, Phone, Position Position Phone but Phone Position EmpIDNamePhonePosition E0045Smith1234Clerk E1847John9876Salesrep E1111Smith9876Salesrep E9999Mary1234Lawyer

22. In General To check A  B, erase all other columns check if the remaining relation is many-one (called functional in mathematics) Note: this is the mathematical definition of a function. Book is wrong.

23. Example EmpIDNamePhonePosition E0045Smith1234Clerk E1847John9876Salesrep E1111Smith9876Salesrep E9999Mary1234Lawyer

24. Typical Examples of FDs Product: name  price, manufacturer Person: ssn  name, age Company: name  stockprice, president

25. Formal definition of a key A key is a set of attributes A 1,..., A n s.t. for any other attribute B, A 1,..., A n  B A minimal key is a set of attributes which is a key and for which no subset is a key Note: book calls them superkey and key

26. Examples of Keys Product(name, price, category, color) name, category  price category  color Keys are: {name, category} and all supersets Enrollment(student, address, course, room, time) student  address room, time  course student, course  room, time Keys are: [in class]

27. Finding the Keys of a Relation Given a relation constructed from an E/R diagram, what is its key? Rules: 1. If the relation comes from an entity set, the key of the relation is the set of attributes which is the key of the entity set. address namessn Person Person(address, name, ssn)

28. Finding the Keys Person buys Product name pricenamessn buys(name, ssn, date) date Rules: 2. If the relation comes from a many-many relationship, the key of the relation is the set of all attribute keys in the relations corresponding to the entity sets

29. Finding the Keys Except: if there is an arrow from the relationship to E, then we don’t need the key of E as part of the relation key. Purchase Product Person Store Payment Method name card-no ssn sname Purchase(name, sname, ssn, card-no)

30. Finding the Keys More rules: Many-one, one-many, one-one relationships Multi-way relationships Weak entity sets (Try to find them yourself, or check book)