1. CSE544 Data Modeling, Conceptual Design
Wednesday, April 7, 2004

2. Outline
ER diagrams (Chapter 2)
Conceptual Design (Chapter 19)

3. Database Design Data Modeling SQL Tables Refinement Files E/R diagrams
Relations

4. Relational Schema Design
Person
buys
Product
name
price
ssn
Conceptual Model:
Relational Model:
plus FD’s
Normalization:
Eliminates anomalies

5. Entity / Relationship Diagrams
Attributes
address
Entity sets
Product
buys
Relationships

6. name
category
name
price
makes
Company
Product
stockprice
buys
employs
Person
name
ssn
address

7. Keys in E/R Diagrams Every entity set must have a key name category
price
Product

8. Multiplicity of E/R Relations
one-one:
many-one
many-many 1 2 3 a b c d 1 2 3 a b c d 1 2 3 a b c d

9. name
category
name
price
makes
Company
Product
stockprice
What does this say ?
buys
employs
Person
name
ssn
address

10. Multi-way Relationships
Purchase
Product
Person
Store

11. Arrows in Multiway Relationships
Q: what does the arrow mean ?
Rental
VideoStore
Person
Movie
Invoice
A: if I know the store, person, invoice, I know the movie too

12. Arrows in Multiway Relationships
Q: what do these arrow mean ?
Invoice
VideoStore
Rental
Movie
Person
A: store, person, invoice determines movie and store, invoice, movie determines person

13. Arrows in Multiway Relationships
Q: how do I say: “invoice determines store” ?
A: no good way; best approximation:
Incomplete (why ?)
Rental
VideoStore
Person
Movie
Invoice

14. Roles in Relationships
What if we need an entity set twice in one relationship?
Product
Purchase
Store
buyer
salesperson
Person

15. Attributes on Relationships
date
Product
Purchase
Store
Person

16. Converting Multi-way Relationships to Binary
ProductOf
date
Product
Purchase
StoreOf
Store
BuyerOf
Person
Need arrows here !
Which direction ?

17. From E/R Diagrams to Relational Schema
Entity set  relation
Relationship  relation

18. Entity Set to Relation name category price Product
Product(name, category, price)
name category price
gizmo gadgets $19.99

19. Relationships to Relations
price
name
category
Start Year
name
makes
Company
Product
Stock price
Makes(product-name, product-category, company-name, year)
(watch out for attribute name conflicts)

20. Relationships to Relations
price
name
category
Start Year
name
makes
Company
Product
Stock price
No need for Makes. Modify Product:
Product(name, category, price, startYear, companyName)

21. Multi-way Relationships to Relations
address
name
Product
Purchase
price
Store
name
Purchase(prodName,stName,ssn)
Person
ssn
name

22. Design Principles What’s wrong? Purchase Product Person President
Country
Person
Moral: be faithful!

23. Design Principles: What’s Wrong?
date
Product
Purchase
Store
Moral: pick the right
kind of entities.
personAddr
personName

24. Design Principles: What’s Wrong?
date
Dates
Product
Purchase
Store
Moral: don’t
complicate life more
than it already is.
Person

25. Subclasses name category price Product isa isa Software Product
Educational Product
platforms
Age Group

26. Subclasses to Relations
Product
Name
Price
Category
Gizmo 99
gadget
Camera 49
photo
Toy 39
Product
name
category
price
isa
Educational Product
Software Product
Age Group
platforms
Sw.Product
Name
platforms
Gizmo
unix
Ed.Product
Name
Age Group
Gizmo
todler
Toy
retired
Notice: subclass = subset
Alternative: disjoint classes (Java, C++)

27. Modeling UnionTypes With Subclasses
FurniturePiece
Person
Company
Each piece of furniture is owned either by a person, or by a company

28. Modeling Union Types with Subclasses
Solution 1. Acceptable, imperfect (What’s wrong ?)
FurniturePiece
Person
Company
ownedByPerson

29. Modeling Union Types with Subclasses
Solution 2: better
Owner
isa
isa
ownedBy
Person
Company
FurniturePiece

30. Referential Integrity Constraints
makes
Product
Company
Each product made by at most one company.
Some products made by no company
makes
Product
Company
Each product made by exactly one company.

31. Other Constraints
makes
<100
Product
Company
What does this mean ?

32. Weak Entity Sets Entity sets are weak when their key comes from other
classes to which they are related.
affiliation
Team
University
sport
number
name
University(name)
Team(universityName, number, sport)

33. Weak Entity Sets R1 E3 E1 A3 A1 A2 R2 B3 E2 R3 What are the keys ? E4

34. Schema Refinement For the relational model Relation: R(A1, A2, …, Am)
Schema: relation name, attribute names
Instance: a mathematical m-ary relation
Database: R1, R2, …, Rn
Schema
Instance
Schema refinement = normalization

35. First Normal Form (1NF)
A database schema is in First Normal Form if all tables are flat
Student
Student
Name
GPA
Alice
3.8
Bob
3.7
Carol
3.9
Name
GPA
Courses
Alice
3.8
Bob
3.7
Carol
3.9
Math DB OS
Takes
Course
Student
Course
Alice
Math
Carol DB
Bob OS
Course
Math DB OS DB OS
May need to add keys
Math OS

36. More Normal Forms Based on Functional Dependencies
2nd Normal Form (obsolete)
3rd Normal Form
Boyce Codd Normal Form (BCNF)
Based on Multivalued Dependencies
4th Normal Form
Based on Join Dependencies
5th Normal Form
Discuss next

37. Functional Dependencies
A form of constraint
hence, part of the schema
Finding them is part of the database design

38. Functional Dependencies
Functional Dependency:
A1, A2, …, An  B1, B2, …, Bm
Meaning:
If two tuples agree on the attributes
then they must also agree on the attributes
A1, A2, …, An
B1, B2, …, Bm

39. Functional Dependencies
Definition: A1, ..., An  B1, ..., Bm holds in R if:
t, t’  R, (t.A1=t’.A1  ...  t.An=t’.An  t.B1=t’.B1  ...  t.Bm=t’.Bm ) R A1
... An B1 Bm t
if t, t’ agree here
then t, t’ agree here t’

40. Examples EmpID  Name, Phone, Position Position  Phone
but Phone  Position
E0045
Smith
1234
Clerk
E1847
John
9876
Salesrep
E1111
Smith
9876
Salesrep
E9999
Mary
1234
Lawyer

41. Example Product(name, category, color, department, price)
Consider these FDs:
name  color
category  department
color, category  price
What do they say ?

42. Example FD’s are constraints: On some instances they hold name  color
On others they don’t
name  color
category  department
color, category  price
name
category
color
department
price
Gizmo
Gadget
Green
Toys 49
Tweaker 99
No: color,category  price doesn’t hold
Does this instance satisfy all the FDs ?

43. Example name  color category  department color, category  price
Gizmo
Gadget
Green
Toys 49
Tweaker
Black 99
Stationary
Office-supp. 59
yes
What about this one ?

44. Inference If some FDs are satisfied, then others are satisfied too
name  color
category  department
color, category  price
If all these FDs are true:
Then this FD also holds:
name, category  price
Why ??
We say that the new FD is implied

45. Armstrong’s Axioms Splitting rule and Combing rule
A1, A2, …, An  B1, B2, …, Bm
Splitting rule
and
Combing rule
Is equivalent to A1
... An B1 Bm
A1, A2, …, An  B1
A1, A2, …, An  B2
A1, A2, …, An  Bm

46. Armstrong’s Axioms Trivial Rule A1, A2, …, An  Ai
where i = 1, 2, ..., n A1 … Am
Why ?

47. Armstrong’s Axioms Transitive Closure Rule If
A1, A2, …, An  B1, B2, …, Bm
Why ?
and
B1, B2, …, Bm  C1, C2, …, Cp
then
A1, A2, …, An  C1, C2, …, Cp A1 … An B1 Bm C1
... Cp

48. Example (continued) 1. name  color 2. category  department
3. color, category  price
To:
name, category  price
From:
Inferred FD
Which Rule did we apply ?
4. name, category  name
5. name, category  color
6. name, category  category
7. name, category  color, category
8. name, category  price

49. Example (continued) 1. name  color 2. category  department
3. color, category  price
Answers:
Inferred FD
Which Rule did we apply ?
4. name, category  name
Trivial rule
5. name, category  color
Transitivity on 4, 1
6. name, category  category
7. name, category  color, category
Split/combine on 5, 6
8. name, category  price
Transitivity on 3, 7

50. Closure of a Set of FDs
Definition. Given a set F of functional dependencies, the closure, F+, denotes all FDs implied by F
Theorem. Armstrong axioms are sound and complete for computing F+
What do sound and complete mean ?
Sound = if Armstrong’s axioms derive some functional dependency X -> Y, then X->Y is indeed implied by F
Complete = if some functional dependency X->Y is implied by F, then there exists a sequence of steps that allow us to derive X->Y from Armstrong’s axioms

51. Variation Augmentation A1, A2, …, An  B If then
A1, A2, …, An , C1, C2, …, Cp  B
Augmentation follows from trivial rules and transitivity How ?

52. Problem: Compute F+ Given F compute its closure F+. How to proceed ?
Apply Armstrong’s Axioms repeatedly
Better: use the Closure Algorithm for a set of attributes (next)

53. Closure of a set of Attributes
Given a set of attributes A1, …, An
The closure, {A1, …, An}+ , is the set of attributes B s.t. A1, …, An  B
Example:
name  color
category  department
color, category  price
Closures: name+ = {name, color} {name, category}+ = {name, category, color, department, price} color+ = {color}

54. Closure Algorithm (for Attributes)
Start with X={A1, …, An}.
Repeat until X doesn’t change do:
if B1, …, Bn  C is a FD and
B1, …, Bn are all in X
then add C to X.
Example:
name  color
category  department
color, category  price
{name, category}+ = {name, category, color, department, price}

55. Example In class: A, B  C R(A,B,C,D,E,F) A, D  E B  D A, F  B
Compute {A,B}+ X = {A, B, }
Compute {A, F}+ X = {A, F, }

56. Closure Algorithm (for FDs)
Example:
A, B  C A, D  B
B  D
Step 1: Compute X+, for every X:
A+ = A, B+ = BD, C+ = C, D+ = D
AB+ = ABCD, AC+ = AC, AD+ = ABCD
ABC+ = ABD+ = ACD+ = ABCD (no need to compute– why ?)
BCD+ = BCD, ABCD+ = ABCD
Step 2: Enumerate all FD’s X  Y, s.t. Y  X+ and XY = :
AB  CD, ADBC, ABC  D, ABD  C, ACD  B

57. Keys
A superkey is a set of attributes A1, ..., An s.t. A1, ..., An  B for all attributes B
A key is a minimal superkey

58. Computing Keys Compute X+ for all sets X
If X+ = all attributes, then X is a superkey
Consider only the minimal superkeys
Note: there can be exponentially many keys !
Example: R(A,B,C), ABC, BCA Keys: AB and BC

59. Examples of Keys Product(name, price, category, color)
name, category  price
category  color
Key: {name, category} Superkeys: supersets
Enrollment(student, address, course, room, time)
student  address
room, time  course
student, course  room, time
Keys are: [in class]
Keys: {student, room, time}, {student, course} and all supersets

60. Incomplete (what does it say ?)
FD’s for E/R Diagrams
Say: “the CreditCard determines the Person”
Product
sname
Purchase
name
Store
Incomplete (what does it say ?)
card-no
CreditCard
Person
ssn
Purchase(name , sname, ssn, card-no)
card-no  ssn

61. Data Anomalies When a database is poorly designed we get anomalies:
Redundancy: data is repeated
Updated anomalies: need to change in several places
Delete anomalies: may lose data when we don’t want
Schema refinement means removing the data anomalies.

62. Data Anomalies Anomalies:
Recall set attributes (persons with several phones):
Name
SSN
PhoneNumber
City
Fred
Seattle
Joe
Westfield
SSN  Name, City
but not SSN  PhoneNumber
Anomalies:
Redundancy = repeat data
Update anomalies = Fred moves to “Bellevue”
Deletion anomalies = Joe deletes his phone number: what is his city ?

63. Relation Decomposition
Break the relation into two:
Name
SSN
PhoneNumber
City
Fred
Seattle
Joe
Westfield
Name
SSN
City
Fred
Seattle
Joe
Westfield
SSN
PhoneNumber
Anomalies have gone:
No more repeated data
Easy to move Fred to “Bellevue” (how ?)
Easy to delete all Joe’s phone number (how ?)

64. Decompositions in General
R(A1, ..., An, B1, ..., Bm, C1, ..., Cp)
R1(A1, ..., An, B1, ..., Bm)
R2(A1, ..., An, C1, ..., Cp)
R1 = projection of R on A1, ..., An, B1, ..., Bm
R2 = projection of R on A1, ..., An, C1, ..., Cp

65. Problems With Decomposition
Can we get the data back correctly ?
Lossless decomposition
Discuss next
Can we recover the FD’s on the ‘big’ table from the FD’s on the small tables ?
Dependency-preserving decomposition
Figure out yourself, or read

66. Lossless Decomposition
Sometimes it is correct:
Name
Price
Category
Gizmo
19.99
Gadget
OneClick
24.99
Camera
Name
Price
Gizmo
19.99
OneClick
24.99
Name
Category
Gizmo
Gadget
OneClick
Camera

67. Lossy Decomposition Sometimes it is not: What’s wrong ?? Name Price
Category
Gizmo
19.99
Gadget
OneClick
24.99
Camera
What’s wrong ??
Name
Category
Gizmo
Gadget
OneClick
Camera
Price
Category
19.99
Gadget
24.99
Camera

68. Decompositions in General
R(A1, ..., An, B1, ..., Bm, C1, ..., Cp)
R1(A1, ..., An, B1, ..., Bm)
R2(A1, ..., An, C1, ..., Cp)
Theorem If A1, ..., An  B1, ..., Bm
Then the decomposition is lossless
Note: don’t need necessarily A1, ..., An  C1, ..., Cp
Example: name  price, hence the first decomposition is lossless

69. Normal Forms Decomposition into Boyce Codd Normal Form (BCNF)
Losselss
Decomposition into 3rd Normal Form
Losless
Dependency preserving

70. Boyce-Codd Normal Form
A simple condition for removing anomalies from relations:
A relation R is in BCNF if:
If A1, ..., An  B is a non-trivial dependency
in R , then {A1, ..., An} is a superkey for R
Equivalently: for any set of attributes X, either X+ = X or X+ = all attributes

71. BCNF Decomposition Algorithm
Repeat choose A1, …, Am  B1, …, Bn that violates the BNCF condition split R into R1(A1, …, Am, B1, …, Bn) and R2(A1, …, Am, [rest]) continue with both R1 and R2 Until no more violations
Heuristics: choose B1, …, Bn “as large as possible”
Is there a
2-attribute
relation that is
not in BCNF ?
B’s
A’s
rest
Note: need to compute the FDs on R1, R2 (how ?) R1 R2

72. BCNF Example FD: SSN  Name, City Key: {SSN, PhoneNumber}
Fred
Seattle
Joe
Westfield
FD: SSN  Name, City
Key: {SSN, PhoneNumber}
Is it in BCNF?
Another way: SSN+ ={SSN, Name, City} but no PhoneNumber

73. BCNF Example SSN  Name, City Let’s check anomalies: Redundancy ?
Fred
Seattle
Joe
Westfield
SSN  Name, City
Let’s check anomalies:
Redundancy ?
Update ?
Delete ?
SSN
PhoneNumber

74. Example R(A,B,C,D) A  B, B  C Key: AD
Violations of BCNF: A  B, A C, ABC, B  C
Pick A BC first: split into R1(A,B,C) R2(A,D)
In R1 : B  C; split into R11(A,B), R12(B,C)
Final answer: R11(A,B), R12(B,C), R2(A,D)

75. Example (cont’d) R(A,B,C,D) A  B, B  C Order matters !
Pick A C first: R1(A,C), R2(A,B,D)
In R2: A  B; decompose into R21(A,B), R22(A,D)
Final answer: R1(A,C), R21(A,B), R22(A,D)
Which one is better ?
Answer: the first decomposition is better, because it is dependency preserving. In the second decomposition we loose the dependency B->C.

76. BCNF and Dependencies FD’s: Unit  Company; Company, Product  Unit
So, there is a BCNF violation, and we decompose.
Unit
Company
Unit  Company
Unit
Product
No FDs
In BCNF we loose the FD: Company, Product  Unit

77. Solution: 3rd Normal Form (3NF)
A simple condition for removing anomalies from relations:
A relation R is in 3rd normal form if :
Whenever there is a nontrivial dependency A1, A2, ..., An  B for R , then {A1, A2, ..., An } a super-key for R,
or B is part of a key.
Please read in the book !!!

78. 3NF Discussion 3NF decomposition v.s. BCNF decomposition: Tradeoffs
Use same decomposition steps, for a while
3NF may stop decomposing, while BCNF continues
Tradeoffs
BCNF = no anomalies, but may lose some FDs
3NF = keeps all FDs, but may have some anomalies