1. One More Normal Form Consider the dependencies: Product Company Company, State Product Is it in BCNF?

2. Multivalued Dependencies (and one last normal form) Name SSN Phone Number Course Fred 123-321-99 (206) 572-4312 CSE-444 Fred 123-321-99 (206) 572-4312 CSE-341 Fred 123-321-99 (206) 432-8954 CSE-444 Fred 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.

3. 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.

4. 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: 

5. 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.

6. 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:

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

8. Projection Unary operation, selects columns Eliminates duplicate tuples Example: project social-security number and names.

10. 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)

12. 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

13. 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

14. 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 products Ex #3: Find names of people who bought American products and did not buy French products Ex #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.

16. 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:

17. Operations on Bags (and why we care) Basic operations: Projection Selection Union Intersection Set difference Cartesian product Join (natural join, theta join)