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

Transcription

1 REVIEW Exam Su 3:30PM - 6:30PM 2010/12/12 Room C ALGEBRA 1

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

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4 10 FUNCTIONAL DEPENDENCY FUNCTIONAL DEPENDENCIES (FDS) A functional dependency X Y 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 K R However, K R does not require K to be minimal! 12 4

5 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 Wages R W S N L R H Attishoo Smiley Smethurst Guldu Madayan S N L R W H Attishoo Smiley Smethurst Guldu Madayan 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,,jid,did,,qty,value), and: C is the key: C CSJDPQV Project purchases a part using single contract: JP C 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 14 Suppose that relation R contains attributes A1... An. A decomposition of 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 15 5

6 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) A B C Relation: ABCDE A B C D Decompose to? 17 Relation: ABCD C D C A B C B 18 6

7 Relation: ABCD B C D A BD 19 Relation: ABCD ABC D D A ABC BCD 20 Relation: ABCD AB C AB D C A D B AB BC CD AD 21 7

8 Suppose you are given a relation R(A,B,C,D) Dependencies AB C C A C D AB BC Decomposed into ACD and BC. Good? Lossless. Can join back to ABCD. Dependency AB C is not preserved. 22 Suppose you are given a relation R(A,B,C,D) Dependencies A BC C AD A C Decomposed into ABC and AD. Good? No. A is key, so no need to decompose. Dependency C AD is not preserved. 23 8