Instructor: Mohamed Eltabakh meltabakh@cs.wpi.edu Normalization- 3NF Part III Instructor: Mohamed Eltabakh meltabakh@cs.wpi.edu

Announcements Homework 2 is due NOW !!! Homework 3 will be out today (Nov. 15) and due on Nov. 22, 8:00AM Midterm on Nov. 22 Until Normalization (Normalization is included) Next lecture is mostly revision + short quiz

Third Normal Form: Motivation There are some situations where BCNF is not dependency preserving Solution: Define a weaker normal form, called Third Normal Form (3NF) Allows some redundancy (we will see examples later) But all FDs can be checked on individual relations without computing a join There is always a lossless-join, dependency-preserving decomposition into 3NF

Normal Form : 3NF Relation R is in 3NF if, for every FD in F+ α  β, where α ⊆ R and β ⊆ R, at least one of the following holds: α → β is trivial (i.e.,β⊆α) α is a superkey for R Each attribute in β-α is part of a candidate key (prime attribute)

Testing for 3NF Use attribute closure to check for each dependency α → β, if α is a superkey If α is not a superkey, we have to verify if each attribute in (β- α) is contained in a candidate key of R

3NF: Example Is relation Lot in 3NF ? Lot (ID, county, lotNum, area, price, taxRate) Candidate key: <county, lotNum> FDs: county  taxRate area  price Is relation Lot in 3NF ? NO Decomposition based on county  taxRate Lot (ID, county, lotNum, area, price) County (county, taxRate) Are relations Lot and County in 3NF ? Lot is not

3NF: Example (Cont’d) Is every relation in 3NF ? Lot (propNo, county, lotNum, area, price) County (county, taxRate) Candidate key for Lot: <county, lotNum> FDs: county  taxRate area  price Decomposition based on area  price Lot (propNo, county, lotNum, area) County (county, taxRate) Area (area, price) Is every relation in 3NF ? YES

Main Idea of the 3NF Decomposition Use the decomposition algorithm as in BCNF But to ensure dependency preservation If α  β is not preserved, then create relation (α, β) where α is the key To ensure the result of decomposition is dependency-preserving and lossless Use the canonical cover in the decomposition 7

Canonical Cover of FDs Given set of FDs (F) with functional closure F+ Canonical Cover (Minimal Cover) = G Is the smallest set of FDs that produce the same F+ There are no extra attributes in the L.H.S or R.H.S of and dependency in G Given set of FDs (F) with functional closure F+ Canonical cover of F is the minimal subset of FDs (G), where G+ = F+ Every FD in the canonical cover is needed, otherwise some dependencies are lost 8

Example : Canonical Cover Given F: A  B, ABCD  E, EF  GH, ACDF  EG Then the canonical cover G: A  B, ACD  E, EF  GH 8

Computing the Canonical Cover Given a set of functional dependencies F, how to compute the canonical cover G Use the next algorithm for this step

Finding Extraneous Attributes

Example : Canonical Cover (Lets Check L.H.S) Given F = {A  B, ABCD  E, EF  G, EF  H, ACDF  EG} Union Step: {A  B, ABCD  E, EF  GH, ACDF  EG} Test ABCD  E Check A: {BCD}+ = {BCD}  A cannot be deleted Check B: {ACD}+ = {A B C D E}  Then B can be deleted Now the set is: {A  B, ACD  E, EF  GH, ACDF  EG} Test ACD  E Check C: {AD}+ = {ABD}  C cannot be deleted Check D: {AC}+ = {ABC}  D cannot be deleted 8

Example: Canonical Cover (Lets Check L.H.S-Cont’d) Now the set is: {A  B, ACD  E, EF  GH, ACDF  EG} Test EF  GH Check E: {F}+ = {F}  E cannot be deleted Check F: {E}+ = {E}  F cannot be deleted Test ACDF  EG None of the H.L.S can be deleted 8

Example: Canonical Cover (Lets Check R.H.S) Now the set is: {A  B, ACD  E, EF  GH, ACDF  EG} Test EF  GH Check G: {EF}+ = {E F H}  G cannot be deleted Check H: {EF}+ = {E F G}  H cannot be deleted Test ACDF  EG Check E: {ACDF}+ = {A B C D F E G}  E can be deleted Now the set is: {A  B, ACD  E, EF  GH, ACDF  G} 8

Example: Canonical Cover (Lets Check R.H.S-Cont’d) Now the set is: {A  B, ACD  E, EF  GH, ACDF  G} Test ACDF  G Check G: {ACDF}+ = {A B C D F E G}  G can be deleted Now the set is: {A  B, ACD  E, EF  GH} The canonical cover is: {A  B, ACD  E, EF  GH} 8

Use of Canonical Cover Used in the decomposition of relations to be in 3NF The resulting decomposition is lossless and dependency preserving

Summary of Normalization Normalization forms First Normal Form (1NF) BCNF Third Normal Form (2NF) Fourth Normal Form (4NF) – Not covered Used to ensure the database design is in a good form Decomposing the relation according to functional dependencies