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- Exam
- Su 3:30PM - 6:30PM 2010/12/12
- Room C9000

Relational Algebra Operations

- Basic operations
- Selection ( ) Selects a subset of rows from relation.
- Projection( ) Deletes unwanted columns from relation.
- Cartesian product( ) Combinetwo relations.
- Set-difference ( ) Tuples in relation 1, but not in relation 2.
- Union( ) Tuples in relation 1 or in relation 2.

Functional Dependencies (FDs)

- A functional dependency XY holds over relation R if, for every allowable instance r of R:
- given two tuples in r, if the X values agree, then the Y values must also agree. (X and Y are sets of attributes.)

- An FD is a statement about all allowable relations.
- Must be identified based on semantics of application.
- Given some allowable instance r1 of R, we can check if it violates some FD f, but we cannot tell if f holds over R!

- K is a candidate key for R means that KR
- However, KR does not require K to be minimal!

Example (Contd.)

- Problems due to R W :
- Update anomaly: Can we change W in just the 1st tuple of SNLRWH?
- Insertion anomaly: What if we want to insert an employee and don’t know the hourly wage for his rating?
- Deletion anomaly: If we delete all employees with rating 5, we lose the information about the wage for rating 5!

Hourly_Emps2

Reasoning About FDs (Contd.)

- Couple of additional rules (that follow from AA):
- Union: If X Y and X Z, then X YZ
- Decomposition: If X YZ, then X Y and X Z

- Example: Contracts(cid,sid,jid,did,pid,qty,value), and:
- C is the key: C CSJDPQV
- Project purchases a part using single contract: JPC
- Dept purchases at most a part from a supplier:SD P

- JP C, C CSJDPQV imply JP CSJDPQV
- SD P implies SDJ JP
- SDJ JP, JP CSJDPQV imply SDJ CSJDPQV

- Suppose that relation R contains attributes A1 ... An. A decompositionof R consists of replacing R by two or more relations such that:
- Each new relation scheme contains a subset of the attributes of R (and no attributes that do not appear in R), and
- Every attribute of R appears as an attribute of one of the new relations.

- e.g., A B, ABCD E, EF GH, ACDF EG has the following minimal cover:
- A B, ACD E, EF G and EF H

Examples

Does A B hold?

Don’t know

Does BC A hold?

Does not hold (first two tuples)

Does B C hold?

Does not hold (last 2 tuples)

Examples

- Relation: ABCDE
- Dependencies:
- Decompose to?

Examples

- Relation: ABCD
- Dependencies:
- What is the candidate key?

Examples

- Relation: ABCD
- Dependencies:
- What is the candidate key?

Examples

- Relation: ABCD
- Dependencies:
- What is the candidate key?

Examples

- Relation: ABCD
- Dependencies:
- What is the candidate key?

Examples

- Suppose you are given a relation R(A,B,C,D)
- Dependencies
- What is the candidate key?
- Decomposed into ACD and BC. Good?

Examples

- Suppose you are given a relation R(A,B,C,D)
- Dependencies
- What is the candidate key?
- Decomposed into ABC and AD. Good?

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