软件学院 Yunsheng Liu 2008.10 Yunsheng Liu 2008.10. Yubsheng-DBS 2 3.1 Introduction 1. Concepts - A DM( data model) is an abstract representation to describe

软件学院软件学院

Yunsheng Liu

2008.10

Yunsheng Liu

2008.10

Yubsheng-DBS 2

3.1 Introduction3.1 Introduction

1. Concepts

- A DM( data model) is an abstract representation to describe (the data of ) a DB in mathematics

2. The elements of a DM: a set of notions with their notations for static

structure a set of operations for dynamic behavior a set of constraints for the structures and behaviors

3. The spectrum of DMs

Yubsheng-DBS 3

Relational DM Logical DMLogical DM

Value-Oriented Model

Ex-RDMEx-RDM

Functional DM

E-R Model

Semantic DMSemantic DM

Permanent-Language OMPermanent-Language OM Query Language OMQuery Language OM

Object Model

Object-Oriented Model

Hierarchical DM

Network DM

Record-Oriented Model

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3.2 The Entity-Relationship Model

3.2 The Entity-Relationship Model

3.2.1 Entity and Entity Set3.2.1 Entity and Entity Set1. Entity concept - An entity is a thing/object in the RW which exists and is

distinguishable from all others — can be identified

2. Entity properties/characteristics - Describing an entity — called Attributes3. Entity type vs. instances - An abstract representation of entities with the

same name and the same set of attributes e.g.: Student(S#, Sname, Sex, Birthday, Dept)

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4. Entity set - A group consisting of all “similar” entities of the

same type that possesses of the same name and attributes

- Entity sets need not be disjoint.5. Examples:

3.2.1 Entity and Entity Set3.2.1 Entity and Entity Set

Entity Entity set A student — All students An airline — All airlines A course — All courses

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……………

Math19931226MWang Z.200010123

CST19970206FLi Y.200515006

SW19981020MZhang X.200610001

DeptBirthdaySexS-nameS#Student

Entity type

An Entity

Entity set

C# C-name Term Dept

SW402 DBS. Fall SW

CS501 ADBT Spring CST

SW302 OS. Fall SW

… … … …

Course

3.2.1 Entity and Entity Set3.2.1 Entity and Entity Set

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3.2.2 Attributes and Domains3.2.2 Attributes and Domains

1. ConceptsProperties or characteristics used to represent

an entityType—(attr-name, attri-type)Value—data value

2. Purposes DescriptionIdentification—Key

Single- and multi-valus Null

— elementary units to form an entity

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3. Simple vs. composite attributes

4. Derived attributes

5. Key — a set of attributes to uniquely identify an entity — key attributes

6. Domain—a set of all the values that an attribute may take

3.2.2 Attributes and Domains3.2.2 Attributes and Domains

Any value in a domain must be elementary

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3.2.3 Relationship and Relationship Set3.2.3 Relationship and Relationship Set

1. Relationship concepts An relationship is an association among two or

more entities. 2-ary relationships vs. n-ary relationships—degree An entity may participate in different kinds of

relationships and also in different relationships of the same type

2. Relationship characteristics - Attributes 3. Relationship type vs. instances - It is similar to that of entities

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4. Relationship set

- A set of relationships of the same type

5. Multiple relationships and multi-value relationships

There exist more than one relationship type/set between two entity sets

There exist more than one relationships between two entities in the same set

e.g.


Multiple relationships

Multi-value relationship

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6. Degree—the number of entity set associated in a Relationship type. e.g. 2-ary, 3-ary, n-ary

n-ary A set of 2-ary relationships

1 : 1 1 : MN : M

College : DeanDept : StudentStudent : Course

e.g.


7. Cardinality—the numbers of entities in variant entity sets appeared in the same relationship

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3.2.4 Identification3.2.4 Identification

1. Identifying entities

Let X is a key of entity set E, then any attribute set X’X can also uniquely identify E. X’ is called a superkey—an attribute set covered a key

Key—the smallest supper key

Supperkey

There may exist more than one key for an entity set. All of them is referred as candidate keys

The chosen one of candidate keys is a primary key

Candidate versus Primary key

Key— an attribute set uniquely identifying single Es

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Whether KA ?? where K= a key attribute set and A= the set of all

the attributes for an entity set

(customer#, restaurant#, time, food) Non-key— K∩A K - Weak entity

Total key — K=A Please give an example. Could you ?


Primary attributes vs. Non-primary attributes -Attribute in a key vs. attributes not in any key

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2. Identifying relationships

- Let R be a relationship set among entity sets E1, …,En

and PKi be the primary key of Ei (i=1,2,..,n). Rule: If R is a single-value relationship, then PK = PKi

If R is a multi-value relationship, R must has its own attributes, saying Ai (i=1,…,m), then

PK = PKi Ai

i =1

n

i =1

m

i =1

n

Examples: G-record( Student, Course, Grade) C-Schedule( Course, Teacher, Time, Room)


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3.2.5 E-R Diagram3.2.5 E-R Diagram

1. Graphic elements

E-name Entity type/set

MN Cardinality of a relationship

Relationship type/setR-name

Attribute typeA-name

xy Key attributes—plus underscore “ ___”

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2. Examples

Grade

Student Hold DeptS#

Sname

Sex Dept

D#

DnamePhoneLoca

1M

Student Enroll CourseS#

Sname

Sex Dept

C#

CnameDeptDate

N M

Locus

3.2.5 E-R Diagram3.2.5 E-R Diagram

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D-name

E-R Diagram of a University DB

ProjectLab

Course

Teacher Student

L-P

LecturingChairing

Advising

Holding

Dividing

Studying

Working

Managing Researching

Holding

M N

N1

M N

N1

M

N

N

1

1

N

1

1

P

N

Main-P Sub-P

1

C-name

C#

S-name

S#

Sex

Bir-dayN

1

Address

Phone

Position

Time

T-name

Phone

Interests

M N

L-name

Address

Phone

P-name

Pro#

S-E time

Budget

T#

Dept

Dependents

family

3.2.6 Extented Features of The E-R Model

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3.2.6 Extended Features of The E-R Model3.2.6 Extended Features of The E-R Model

1. Weak entities/Identifying relationship

Example

Employee Dependentsfamily

They cann’t identify an entity by itselfes. And the identifications have to depend also on the primary attributes of another entity set, called owner entity set.

Identifier relationship ◆ Those between a weak entity and its owner entity ◆ represented by point to the weak entity

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Class hierarchies of entities in an entity set

2. Generalization/Specification relationships

StudentUndergre

GreduateMS_Stud

PhD_Cand

Generalization

Specification

Attributes inheritance

ISA realationship— that between classes at adjacent hierarchies, notated by in E-R model

ISA

ISAIS

A

3.2.6 Extended Features of The E-R Model


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?

Monitoring

3. Aggregation

Relationship among relationships ?

Student CourseTesting

Monitor

Aggregation is an abstraction that considers an association of several objects as an object at a higher level



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3.3 Relational Data Model3.3 Relational Data Model

3.3.1 Introduction3.3.1 Introduction

E.F.Codd, 1970, inaugurating a new age of DB Special notions and terminology for structures,

operations and constraints Powerful mathematical fundamental, Criteria for DB implementation A DB is a collection of relations

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Relation head vs. bodyrelation schema vs.relation type vs. occurrence

A relation schema is a formal description of the logical structure of a relation, like Rname(A1, A2, …, An)

Specifying the rel. name, att. names and domains

Invariable over time

n is called the degree or arity of the relation A relation, called also a table, is a named set of tuples

3.3.2 Terminology— Basic Concepts3.3.2 Terminology— Basic Concepts

1. Relation Entity set

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As entities, an A is a named item, referred to a D A D is a named set of values in the same type Type—pair (Ai : Di) vs.values— aiDi

An A is an atomic element of a relation structureEach is named uniquely in a relation: ij (Ai Aj )

Each Ai takes values from a single domain Di

Multiple attributes may refer to the same domain, i.e. there may exist ij and Di = Dj

2. Attributes(A) and Domains(D)


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4. Graphical show of a relation—Table

3. Tuple Entity

A tuple, called also a row, is an aggregation of the attribute values( one from each attribute).

A list of the attribute values, like (a1, a2,…,an) where

aiDi (i=1,2,…,n), called a component of the tuple

(a1, a2,…,an) is called an n-tuple

Any tuple in a relation is unique


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Student

……………Math19931226MWang Z.200010123

CST19970206FLi Y.200515006

SW19981020MZhang X.200610001

DeptBirthdaySexS-nameS#

Relation schema

Attributes/Collumns

Tuples/Rows

Relation

Attribute values / tuple components

dateM,FM,F String of

digits

D1 String of Chars.

D2 String of Chars.

Dn

Domains

A relation’s tabular show A relation’s tabular show

Attribute names

Relation name

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3.3.3 The General Characteristics of RDB3.3.3 The General Characteristics of RDB

1. All the values in each domain are atomic2. Every attribute is referred to a single domain, but3. A domain may be concerned in different attributes4. Each tuple is uniquely identified ? Key

uniqueness

A DB consists of just relations. How about relationships ?

5. There is no constraint on the number and sequence of tuples in a relation

6. There is no constraint on the number and sequence of attributes in a relation. But ?

7. The schema/head of a relation is fixed8. The body of a relation is variable

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3.3.4 Integrity Constraints3.3.4 Integrity Constraints

1. Keys of a relation A smallest non-empty set of attributes that can

uniquely identify a tuple UniquenessSmallest

Why ?

2. Foreign key of a relation Why ?The relation’s attribute(s) which forms the primary

key of another relation Example: Student(S#, Sname, Sex, Birthday, Dept#)

for relationships between entities

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Reference Integrity:

If R1 holds a foreign key fk which is the primary key of R2 , then any value of fk in R1 is either the primary key value of some tuple in R2 or all Null

3. The Integrity Rules

Why? Could you give an explanation ?

3.3.4 Integrity Constraints3.3.4 Integrity Constraints

Entity Integrity: Any primary(key) attribute value cann’t be Null ?

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3.3.5 Relational Algebra3.3.5 Relational Algebra

Two kinds of notations used for expressing operations on relations:

Algebra notations— Relational algebra

Logical notations— Relational calculusTwo kinds of operations used to form relational

algebra

Conventional set operations

Native relational operations

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Let R1 and R2 be k- and s-arity relations, respectively. Then R3 is a relation consisting of all possible (k+s)-tuples whose first k components form a tupe in R1 and whose last s components form a tuple in R2

1. Basic Relational Algebra Operations - 5 basic operations serving to define relational algebra

(1). Union(U): R1∪R2= R3={t |tR1∨tR2}

(2). Difference(–): R1–R2= R3={t |tR1∧tR2} (3). Cartesian product():

R1R2 =R3 ={t1 t2 | t1R1∧t2R2} R3 is of ?-tuple


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Examples:

R: A B C S: D E F a b d c e b a d b d b e


What is the R×S ?

R×S = T: A B C D E F a b d c e b a b d d b e a d b c e b a d b d b e

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- Native relational operations

(4). Selection(): c(R)={t |tR∧c(t) =.T.}

Where c is a condition expression formed by Operands: constant, attribute names or position

numbers ($-) The arithmetic comparison operators: , ,=,≠.≤,≥, The logical operators: , ,

e.g. Dept ＝’ CS’ Age≤18∧ （ Students）$2 >5 $3≤$1∨ (R)


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A is a list of names or position numbers of the retained attributes, like Ai1

,Ai2,…,Aim

or i1, i2 , …,im

t[A] is a tuple formed by the components of t on AOpposite to ‘SELECT’ being horizontally extracting

tuples, ‘PROJECTION’ is vertically extracting attributes

The duplicate tuples must be removed from the result

(5). Projection(): A(R)={t[A] |tR}

e.g. s-name, sex (Student), 2, 4 (Student)


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Exp is a relational algebra expression. returns the result of Exp, a relation, and assigns

the name R to the result relation and renames the attributes according to the renaming list NList

NList is either a list of items as the following, or a null

oldname→newname or position number→newname

(6). Renaming(): (R(NList), Exp )


2. Additional Relational Algebra Operations

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Examples:

⑴. (S, Student)

⑵. (R3, R1R2 )

⑶. ( Slist(S-name→Name, Dept→Dname),

s-name, dept (Student) )


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(7). Intersection(∩): R1∩R2 = R3={t |tR1∧tR2} R1∩R2 = R1 – (R1 – R2)

(8). Join(⋈) -join (Condition join, ⋈c): R1 ⋈c R2={<t1t2>| t1R1∧t2R2∧c[t1t2]=.T.} c is a condition expression in the form of A B A and B are names or position numbers of some

comparable attributes of R1 and R2, respectively. is a arithmetic comparison operator, such as

＜ ,≤… R1 ⋈c R2 = c (R1R2 )


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Equijoin — the special case of -join where is = R1 ⋈A=B R2 = A=B (R1R2 ) Natural join — the further special case of the equijoin

on common attributes. R ⋈ S =R.A∪S.A - Ac(R.Acom = S.Acom

(RS ))

R.A, S.A are the attribute sets of R and S, respectively, and Acom is their common attribute set

There must exist a common attribute set between the two relations

The duplicate attributes are removed in the result


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3. Composite Operations e.g.:s-name,sex(Dept ＝ CS(Student)) 2,4(3>5(R S)) ∪ 3>5 (2,4 (R S)) ∪ ?


(9). Division(÷)

Let R.A=(X,Y), i.e. the attribute set of R, S.A=(Y), Y and Y are two comparable attribute sets.

R÷S={t|tR[X] (∧ tsS (∃trR ( tr[X]=t t∧ r[Y]=ts[Y’])))}

Where we can get that S.A R.A

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3.4 Network Data Model3.4 Network Data Model

3.4.1 Network Data Objects 3.4.1 Network Data Objects 1. Record type—a named ordered set of data items/fields

Record type Relation types/Entity type

2. Field—a basic named data unit forming a record type

Field (data item) attributes, but

it can be a composite of other fields or a repeated item

3. Link—a relation between two(only two) record types

Link 2-ary relationship in E-R

1:M(all), Ring(comp.), Cycle(all), N:M(comp.),

No n-ary rela.

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3.4.2 Bachman Diagram3.4.2 Bachman Diagram

F-name1…F-namen

Record type LinkL-nameParent

recordChild record

Dept# Dname Add Phone

Dept# Dname Add Phone

OnameAddPhone

OnameAddPhone

LnameAddPhone

LnameAddPhone

C#C#nameTerm

C#C#nameTerm

T#TnamePhone

T#TnamePhone

S#SnameSex

S#SnameSex

Dept

Office Lab Course

Student Teacher

L1

Li

4. Data structure diagram

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3.4.3 Network Structure3.4.3 Network Structure

1. Multiple 1:M relationships all

2. M:N relationshipcomplex net only

3. Ring relationships complex net only

4. Circle relationships not in restricted net

5. N-ary relationships No, creating a relationship- record type and multiple 1:M rel. to each rec. type

6. Class relationship not in restricted net

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3.4.4 DBTG Model3.4.4 DBTG Model

1. CODASYL (Conference on Data System Language ), DBTG (Data Base Task Group) Reports (1971,…,1984…)

2. Simple Network— only 1:M links3. Set ( 系 ) structure A two-level structure consisting of owner record type

and members record types— a link between records Each set must be named, Each set has one and only one owner, and may have

zero, one or more members Any record type may be the owner of a set type and

simultaneously a member of another set type ?

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4. Set type vs. Set occurrences Similar to a relation A set type: SetName(Owner-spec, Member-spec) A set occurrence: a set of an owner and the members

associated with the owner under the set type

3.4.4 DBTG Model3.4.4 DBTG Model

Dept DeptPeople

TeacherTeacherTeacherTeacherStudentStudent

5. Examples:

CourseCourseLecture

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3.5 Hierarchical Data Model3.5 Hierarchical Data Model

IBM,1968, used in they first DBMS IMSThe earliest data model, a special case of the NM

1. Basic Concepts Record type, Field/item, Link— the same as NM DB—forest, a set of trees 2. Hierarchical Data Structures—tree There must be one node without a parent, called a root Any node (except root)must have one and only one

parent. A node may have 0 (leaf), 1 or more children,

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Combined record— virtual record with regular fields, such as ‘Grade’ in the above example

3. Representing M:N relationships with virtual record

Students

Courses

Enroll

N

M

Students

Courses Students

Courses

?

!

3.5 Hierarchical Data Model3.5 Hierarchical Data Model

Students

•

Courses

V-Courses V-Students• Grade Grade

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1. The HM and NM are uniformly referred as Record-based Model

2. The operations in record-based models are GET, INSERT, DELET, MODIFY, etc. and all a-record-at-a-time,

3. There are also integrity constraints, such as - A child record cann’t exist without the parent record For inserting a child record, the parent record must

have already existed, and when deleting a parent record, all the children records

have to be deleted.

3.6 Operations and Integrity in Record-based DM

3.6 Operations and Integrity in Record-based DM

Documents

软件学院 Yunsheng Liu 2008.10 Yunsheng Liu 2008.10. Yubsheng-DBS 2 3.1 Introduction 1. Concepts - A DM( data model) is an abstract representation to describe