Lecture 18 10/09/15. CMPSC431W: Database Management Systems. Instructor: Yu- San Lin

Transcription

1 CMPSC431W: Database Management Systems Lecture 18 10/09/15 Instructor: Yu- San Lin Course Website: hcp:// Slides based on McGraw- Hill & Dr. Wang- Chien Lee 1

2 Dependency- Preserving DecomposiPon (cont.) Let R: a relapon schema that is decomposed into two schemas with acribute sets X and Y F: a set of FDs over R ProjecPon of F on X: the set of FDs in F + that involve only acributes in X Note: U à V in F + is in F X only if all the acributes in U and V are in X 2

3 Dependency- Preserving DecomposiPon (cont.) Defini*on: the decomposipon of relapon schema R with FDs F into schemas with acribute sets X and Y is dependency- preserving if i.e., if we take the dependencies in F X and F Y and compute the closure of their union, we get back all dependencies in F + 3

4 Is this decomposipon dependency- preserving? R ABC F over R = { A à B, B à C, C à A } AB BC 4

5 NormalizaPon We can use algorithms to convert relapons into BCNF or 3NF When converpng R into BCNF It is possible to lossless- join decompose it But not guaranteed to be dependency- preserving While converpng R into 3NF There is always a dependency- preserving and lossless- join decomposipon 5

6 DecomposiPon into BCNF Algorithm: 1. Suppose that R is not in BCNF. Let X R, A be a single acribute in R, and X à A be an FD that causes a violapon of BCNF. Decompose into and. 2. If either R A or XA is not in BCNF, decompose them further by step 1. 6

7 Example of Decomposing into BCNF Contracts (contracpd, supplierid, projecpd, deppd, parpd, qty, value) Schema: CSJDPQV Given FDs: 1. C à CSJDPQV 2. JP à C // ignore this one for now 3. SD à P 4. J à S // add this FD into F CSJDPQV Lossless- join decompose CSJDQV SDP 7

8 Redundancy in BCNF CSJDPQV Lossless- join decompose SD à P not in BCNF CSJDQV SDP in BCNF Lossless- join decompose J à S CJDQV JS JP à C cannot be enforced without a join SoluPon: add a relapon with acribute Storing redundant informapon, but make dependency enforcement cheaper 8

9 Notes on Decomposing into BCNF Choosing different FD to decompose the relapons might lead to different decomposed results There may not always be a dependency decomposipon into BCNF. For example: R SBD F over R = { SB à D, D à B } 9

10 DecomposiPon into 3NF The algorithm for decomposipon into BCNF can be used to obtain a lossless- join decomposipon into 3NF, but dependency preservapon is not ensured Two solupons: 1) If X à Y is not preserved, add relapon XY - XY might violate 3NF 2) Instead of using F, use a for F 10

11 Minimal Cover for F A minimal cover for a set F of FDs is a set G of FDs such that: 1. Every dependency in G is of the form X à A, where A is a single acribute 2. F + = G + 3. If we modify G by delepng an FD or by delepng acributes from an FD in G, the closure changes 11

12 Minimal Cover for F (cont.) Minimal cover for a set of FDs is an equivalent set of FDs that is minimal in two aspects: 1) Every FD is as small as possible : each acribute on the les side is necessary and the right side is a single acribute 2) Every dependency in it is required for the closure to be equal to F + 12

13 Minimal Cover Example #1 Given the FDs in F, find the minimal cover: A à B, ABCD à E, EF à G, EF à H, ACDF à EG 13

14 Algorithm for Obtaining Minimal Cover 1. Put the FDs in a standard form - Single acribute on the right side - Use decomposipon axiom 2. Minimize the les side of each FD - Check each acribute in the les side to see if delepng it will spll preserve G + = F + 3. Delete redundant FDs - Check each FD to see whether it can be deleted and spll preserve G + = F + 14

15 Minimal Cover Example #2 Given the FDs in F, find the minimal cover: ABCD à E, E à D, A à B, AC à D 15

16 Dependency- Preserving DecomposiPon in 3NF To obtain a lossless- join and dependency- preserving decomposipon in 3NF relapons: Let: - R (with a set of F that is minimal cover) decomposed into R 1, R 2,, R n (all in 3NF) - F i : the projecpon of F onto the acributes of R i Do the following: - IdenPfy the set N of dependencies in F that is not preserved - For each FD X à A in N, create a relapon schema XA and add it to the decomposipon of R 16

17 Dependency- Preserving DecomposiPon in 3NF (cont.) Note that all of the added XA are in 3NF as well As an oppmizapon, if N contains several FD with the same les side, we can merge the right side (union axiom) Example: X à A X à B X à C X à ABC 17

18 Decompose into 3NF that is lossless- join and dependency- preserving Schema: CSJDPQV F = { C à CSJDPQV, JP à C, SD à P, J à S } 18

19 Don t Forget Homework 3 and due in two weeks (10/23) Bring your laptop next Monday for more MySQL Project phase 2 presentapon next Thursday (10/15) in the evening 19