Extracting Tables from ERD

A Table Example

• t1 = (foo,bar,baz,{x,y})• t2 = (quz,bar,foo,{y,z})

• t1[a1] = (baz)• t2[a2] = ({y,z})

• t1[a%] = (baz,{x,y})• t2[k%] = (quz,bar)

a2 a1 k2 k1

{x,y} baz bar foo

{y,z} foo bar quz

t1

t2

k' = (k1,k2)a% = (a1,a2)

Vector of all key attributes

Vector of all non-key

attributes

Entities

• A short representation:

E

k1 kn a1 am

k' = (k1,…,kn) a% = (a1,…,am)

E

k' a%

Entities

• Translation to a table:a̅� k

am … a1 kn … k1

E

k' a%

• Constraints:t1[k] = t2[k] t⇒ 1[a%] = t2[a%]

Entities

• We assume k' can not be empty• a% may be empty

E

k' a%

Entities

• Any ai may be multi-valued– Multi-valued attributes cannot be a part of the key

• In domain D, for a table row t:– for an attribute ai: t[ai] D∈

– for a multi-valued attribute aj: t[aj] P(D) ∈• a powerset.

E

k1 kn a1 am

ai

Another Representation of a Multi-Valued Attribute

• A table without multi-valued attributes:

• Tables - one for each multi-valued attribute:

• Specifically for screenshots a power set won't work well

movie

name year screenshots genre

a̅� k

genre year name

Drama 2003 Cold Mountain

k

screenshots year name

screenshot1 2003 Cold Mountain

Relationships

• Each k', a% may be empty• Translation to a table:

E1

k'1 a%1

k'2 a%R k'R k'1

R E2

k'R a%R k'2 a%2

Relationships

• Constraints:– πk2(E2) π⊆ k2(R)

– πk2(R) π⊆ k2(E2) (true for a̅ny relationship!)

– πk1(R) π⊆ k1(E1) (true for a̅ny relationship!)

E1

k'1 a%1

R E2

k'R a%R k'2 a%2

Aggregations

• Turns the relationship into an entity with attributes of the relationship

E1

k'1 a%1

R E2

k'R a%R k'2 a%2

ER

E3

k'3 a%3

Sk'S

a%S

AggregationsE1:

E2:

E3:

a%1 k'1

a%2 k'2

a%3 k'3

a%R k'R k'2 k'1

a%S k'S k'R k'3 k'2 k'1

R:

S:

Example

Network.name traker.name

tracking

intrested1

cause User.name Network.name traker.name

user

name Birth_date

connected network

name type

tracker

name country

interested1cause tracking

Weak EntitiesTranslation to tables:

E1k'1a%1

a%1 k'1

E2k'2a%2

E3k'3a%3

a%2 k'2 k'1

a%3 k'3 k'2 k'1

Weak Entities

Constraints:πk1(E2) ⊆ πk1(E1)

πk1,k2(E3) π⊆ k1,k2(E2)

E1k'1a%1

E2k'2a%2

E3k'3a%3

Example

Address na̅me

Haifa, Hagalil 2 company1

Number na̅me

1 company1

2 company1

companyname1

Address

DepartmentNumber

ISA

• ISA – a branching weak entity without key components in the subclass

E1

k'1 a%1

E2a%2 E3 a%3

ISA

superclass

subclasssubclass

ISA – Translations and ConstraintsDessert:

Ice cream:

Cake:

Constraints:πname(Cake) π⊆ name(Dessert)

πname(Ice cream) π⊆ name(Dessert)

calories name

flavor name

type name

Dessert

name calories

Ice cream

flavor

Cake

type

ISA ISA

Exclusive ISAIce cream:

Sorbet:Frozen_yogurt:

Constraints:πname(Sorbet) π⊆ name(Ice cream)

πname(Frozen_yogurt) π⊆ name(Ice cream)

πna̅me(Sorbet)∩πna̅me(Frozen_yogurt)=∅

Ice cream

name calories

Sorbet

fruit

Frozen_yogurt

additions

ISA

calories name

fruit name

additions name

Covering All ISAIce cream:

Sorebt:

Frozen_yogurt:

Constraints:πname(Sorbet)∩πname(Frozen_yogurt)=∅

Ice cream

Name Calories

Sorbet

fruit

Frozen_yogurt

additions

ISA Thick lines

NO Table!

fruit calories name

additions calories name