lecture17 10/07/15 - penn state college of...

CMPSC431W: Database Management Systems

Instructor: Yu-‐San Lin [email protected]

Course Website: hCp://www.cse.psu.edu/~yul189/cmpsc431w

Slides based on McGraw-‐Hill & Dr. Wang-‐Chien Lee

Lecture 17 10/07/15

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1NF, 2NF & 3NF

•  1NF (remove non-‐atomic values) – Test: should not have non-‐atomic aCributes – Remedy: create relaWons for each non-‐atomic aCribute

•  2NF (remove parWal dependency) – Test: no non-‐key aCributes be funcWonally dependent on a part of the primary key

– Remedy: decompose and create a new relaWon for each parWal dependency

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1NF, 2NF & 3NF (cont.)

•  3NF (remove transiWve dependency) – Test: should not have a non-‐key aCribute funcWonally determined by another (or a set of) non-‐key aCributes

– Remedy: decompose and create a relaWon that includes the non-‐key aCributes that funcWonally determines other non-‐key aCributes

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Boyce-‐Codd Normal Form (BCNF)

•  RelaWon R with FDs F is in BCNF if, for all X à A in F+ – A ∈ X (called a trivial FD), OR –  X contains a key for R (i.e., X is a superkey)

•  IntuiWvely: the only nontrivial dependencies are those in which a _____ determines some aCribute(s) –  Each tuple can be seen as an enWty or relaWonship, idenWfied by a key and described by aCributes

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•  If we use ovals to denote aCributes or sets of aCributes and draw arcs to indicate FDs, a relaWon in BCNF has the structure:

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Key Non-‐key aCr 1

Non-‐key aCr 2

Non-‐key aCr k

…


•  BCNF ensures that no redundancy at all can be detected using FD

•  Example:

– Given X à A, we know the value for ? is _____ – Then, is this instance in BCNF?

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X Y A

x y1 a

x y2 ?

ProperWes of DecomposiWons

•  It is important to check that a decomposiWons does not introduce new problems

•  We should check whether a decomposiWon – allows us to _______ the original relaWon – allows us to check _________________efficiently

•  Two types of decomposiWon: – ___________________ decomposiWon – ___________________ decomposiWon

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Lossless-‐Join DecomposiWon

Defini1on: A decomposiWon of R into two schemas with aCribute sets X and Y is said to be a lossless-‐join decomposiWon with respect to F if, for every instance r of R that saWsfies the dependencies in F,

i.e., we can recover the original relaWon from the decomposed relaWons

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Lossless-‐Join DecomposiWon (cont.)

•  The definiWon can easily be extended to cover a decomposiWon of R into more than two relaWons, since

* Note that the other direcWon does not hold

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Is this decomposiWon lossless-‐join?

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S P D

s1 p1 d1

s2 p2 d2

s3 p1 d3

Instance r

S P

s1 p1

s2 p2

s3 p1

P D

p1 d1

p2 d2

p1 d3

πSP(r) πPD(r)

πSP(r) ⋈ πPD(r)

Revert back

S P D

s1 p1 d1

s2 p2 d2

s3 p1 d3

s1 p1 d3

s3 p1 d1

Decompose into

We call such decomposiWon _____

Theorem 3

Let R be a rela*on and F be a set of FDs that hold over R. The decomposi*on of R into rela*ons with a;ribute sets R1 and R2 is lossless is and only if F+ contains either: •  _______________, OR •  _______________

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Use this simple test to check whether a decomposiWon is lossless

Is this decomposiWon lossless-‐join?

•  Use Theorem 3 to check:

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ssn name lot ra1ng hourly_wages hours_worked

123-‐22-‐3666 Aoshoo 48 8 10 40

231-‐31-‐5368 Smiley 22 8 10 30

131-‐24-‐3650 Smethurst 35 5 7 30

434-‐26-‐3751 Guldu 35 5 7 32

612-‐67-‐4134 Madayan 35 8 10 40

ssn name lot ra1ng hours_worked

123-‐22-‐3666 Aoshoo 48 8 40

231-‐31-‐5368 Smiley 22 8 30

131-‐24-‐3650 Smethurst 35 5 30

434-‐26-‐3751 Guldu 35 5 32

612-‐67-‐4134 Madayan 35 8 40

ra1ng hourly_wages

8 10

5 7

Lossless-‐Join’s ObservaWon #1

If an FD X ! Y holds over a rela*on R and X ∩ Y is empty, the decomposi*on of R into R – Y and XY is lossless. * X appears in both R – Y (since X ∩ Y is empty) and XY, and it is a ____ for XY.

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Lossless-‐Join’s ObservaWon #2

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R Lossless-‐join decompose

R1

R2

Lossless-‐join decompose

R11

R12

Dependency-‐Preserving DecomposiWon

•  Is this in BCNF?

Contracts (contracWd, supplierid, projecWd, depWd, parWd, qty, value) Schema: CSJDPQV Given FDs: 1.  C à CSJDPQV 2.  JP à C 3.  SD à P

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Dependency-‐Preserving DecomposiWon (cont.)

However: Enforcing JP à C into the decomposed relaWons requires an expensive join of the two relaWons whenever a tuple is inserted. è Such decomposiWon ______ dependency-‐preserving

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CSJDPQV

Lossless-‐join decompose CSJDQV

SDP


•  Let – R: a relaWon schema that is decomposed into two schemas with aCribute sets X and Y

– F: a set of FDs over R •  ProjecWon of F on X: the set of FDs in F+ that involve only aCributes in X

•  Note: U à V in F+ is in FX only if all the aCributes in Y and V are in X

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Defini1on: the decomposiWon of relaWon 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 FX and FY and compute the closure of their union, we get back all dependencies in F+

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Is this decomposiWon dependency-‐preserving?

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AB

BC

ABC R

F over R = { A à B, B à C, C à A

}

Don’t Forget

•  Homework 3 will be posted this Friday (10/9) and due in two weeks (10/23)

•  Project phase 2 presentaWon next Thursday (10/15) in the evening🍕

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lecture*17* 10/07/15 - penn state college of...

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lecture17 10/07/15 - penn state college of...