One More Normal Form

• Consider the dependencies:

Product Company

Company, State Product

• Is it in BCNF?

Multivalued Dependencies (and one last normal form)

Name SSN Phone Number Course

Fred 123-321-99 (206) 572-4312 CSE-444Fred 123-321-99 (206) 572-4312 CSE-341Fred 123-321-99 (206) 432-8954 CSE-444Fred 123-321-99 (206) 432-8954 CSE-341

The multivalued dependencies are:

Name, SSN Phone Number Name, SSN Course

4th Normal form: replace FD by MVD.

Querying the Database• How do we specify what we want from our

database?

Find all the employees who earn more than $50,000 and pay taxes in New Jersey.

• We design high-level query languages:– SQL (used everywhere)– Datalog (used by theoreticians and their students)

• Relational algebra: a basic set of operations on relations that provide the basic principles.

Relational Algebra at a Glance• Operators: sets as input, new set as output

• Basic Set Operators– union, intersection, difference, but no complement.

• Selection:• Projection:

• Cartesian Product: X• Joins (natural,equi-join, theta join, semi-join)

• Renaming:

Set Operations• Binary operations

– Result is table(set) with same attributes

• Watch our for naming of attributes in resulting relation.

• Union: all tuples in R1 or R2• Intersection: all tuples in R1 and R2• Difference: all tuples in R1 and not in R2• No complement. Why?• Bags later.

Selection

• Produce a subset of the tuples in a relation which satisfy a given condition

• Unary operation… returns set with same attributes, but ‘selects’ rows

• Use and, or, not, >, <… to build condition

• Find all employees with salary more than $40,000:

Selection Example

EmployeeSSN Name DepartmentID Salary999999999 John 1 30,000777777777 Tony 1 32,000888888888 Alice 2 45,000

SSN Name DepartmentID Salary888888888 Alice 2 45,000

Find all employees with salary more than $40,000.

Projection

• Unary operation, selects columns

• Eliminates duplicate tuples

• Example: project social-security number and names.

Projection Example

EmployeeSSN Name DepartmentID Salary999999999 John 1 30,000777777777 Tony 1 32,000888888888 Alice 2 45,000

SSN Name999999999 John777777777 Tony888888888 Alice

Cartesian Product

• Binary Operation

• Result is tuples combining any element of R1 with any element of R2, for R1XR2

• Schema is union of Schema(R1) & Schema(R2)

Cartesion Product Example

EmployeeName SSNJohn 999999999Tony 777777777

DependentsEmployeeSSN Dname999999999 Emily777777777 Joe

Employee_DependentsName SSN EmployeeSSN DnameJohn 999999999 999999999 EmilyJohn 999999999 777777777 JoeTony 777777777 999999999 EmilyTony 777777777 777777777 Joe

Join (Natural)• Most important, expensive and exciting.

• Combines two relations, selecting only related tuples

• Equivalent to a cross product followed by selection

• Resulting schema has all attributes of the two relations, but one copy of join condition attributes

Complex Queries

Product ( name, price, category, maker)Purchase (buyer, seller, store, product)Company (name, stock price, country)Person( name, phone number, city)

Find phone numbers of people who bought gizmos from Fred.

Find telephony products that somebody bought

Exercises

Product ( name, price, category, maker)Purchase (buyer, seller, store, product)Company (name, stock price, country)Person( name, phone number, city)

Ex #1: Find people who bought telephony products.Ex #2: Find names of people who bought American productsEx #3: Find names of people who bought American products and did not buy French productsEx #4: Find names of people who bought American products and they live in Seattle.Ex #5: Find people who bought stuff from Joe or bought products from a company whose stock prices is more than $50.

Join Example

EmployeeName SSNJohn 999999999Tony 777777777

DependentsEmployeeSSN Dname999999999 Emily777777777 Joe

Employee_DependentsName SSN DnameJohn 999999999 EmilyTony 777777777 Joe

Other Joins and Renaming

• Theta join: the join involves a predicate– R S

• Semi-join: the attributes of one relation are included in the other.

• Renaming:

Operations on Bags (and why we care)

Basic operations:

Projection Selection Union Intersection Set difference Cartesian product

Join (natural join, theta join)