Ch2

Chapter 2: Entity-Relationship
Model

Entity Sets
Relationship Sets
Design Issues
Mapping Constraints
Keys
E-R Diagram
Extended E-R Features
Design of an E-R Database Schema
Reduction of an E-R Schema to Tables

Database System Concepts 2.1 ©Silberschatz, Korth and Sudarshan

Entity Sets

A database can be modeled as:
a collection of entities,
relationship among entities.
An entity is an object that exists and is distinguishable from other
objects.
Example: specific person, company, event, plant
Entities have attributes
Example: people have names and addresses
An entity set is a set of entities of the same type that share the
same properties.
Example: set of all persons, companies, trees, holidays


Entity Sets customer and loan
customer-id customer- customer- customer- loan- amount
name street city number


Attributes
An entity is represented by a set of attributes, that is descriptive
properties possessed by all members of an entity set.
Example:
customer = (customer-id, customer-name,
customer-street, customer-city)
loan = (loan-number, amount)

Domain – the set of permitted values for each attribute
Attribute types:
Simple and composite attributes.
Single-valued and multi-valued attributes
E.g. multivalued attribute: phone-numbers
Derived attributes
Can be computed from other attributes
E.g. age, given date of birth


Composite Attributes


Relationship Sets

A relationship is an association among several entities
Example:
Hayes depositor A-102
customer entity relationship set account entity
A relationship set is a mathematical relation among n ≥ 2 entities,
each taken from entity sets
{(e1, e2, … en) | e1 ∈ E1, e2 ∈ E2, …, en ∈ En}

where (e1, e2, …, en) is a relationship
Example:
(Hayes, A-102) ∈ depositor


Relationship Set borrower


Relationship Sets (Cont.)
An attribute can also be property of a relationship set.
For instance, the depositor relationship set between entity sets
customer and account may have the attribute access-date


Degree of a Relationship Set

Refers to number of entity sets that participate in a relationship
set.
Relationship sets that involve two entity sets are binary (or degree
two). Generally, most relationship sets in a database system are
binary.
Relationship sets may involve more than two entity sets.
E.g. Suppose employees of a bank may have jobs
(responsibilities) at multiple branches, with different jobs at
different branches. Then there is a ternary relationship set
between entity sets employee, job and branch
Relationships between more than two entity sets are rare. Most
relationships are binary. (More on this later.)


Mapping Cardinalities
Express the number of entities to which another entity can be
associated via a relationship set.
Most useful in describing binary relationship sets.
For a binary relationship set the mapping cardinality must be
one of the following types:
One to one
One to many
Many to one
Many to many



One to one One to many
Note: Some elements in A and B may not be mapped to any
elements in the other set



Many to one Many to many
Note: Some elements in A and B may not be mapped to any
elements in the other set


Mapping Cardinalities affect ER Design
Can make access-date an attribute of account, instead of a
relationship attribute, if each account can have only one customer
I.e., the relationship from account to customer is many to one,
or equivalently, customer to account is one to many


E-R Diagrams

Rectangles represent entity sets.
Diamonds represent relationship sets.
Lines link attributes to entity sets and entity sets to relationship sets.
Ellipses represent attributes
Double ellipses represent multivalued attributes.
Dashed ellipses denote derived attributes.
Underline indicates primary key attributes (will study later)

E-R Diagram With Composite, Multivalued, and
Derived Attributes


Relationship Sets with Attributes


Roles
Entity sets of a relationship need not be distinct
The labels “manager” and “worker” are called roles; they specify how
employee entities interact via the works-for relationship set.
Roles are indicated in E-R diagrams by labeling the lines that connect
diamonds to rectangles.
Role labels are optional, and are used to clarify semantics of the
relationship


Cardinality Constraints
We express cardinality constraints by drawing either a directed
line (→), signifying “one,” or an undirected line (—), signifying
“many,” between the relationship set and the entity set.
E.g.: One-to-one relationship:
A customer is associated with at most one loan via the relationship
borrower
A loan is associated with at most one customer via borrower


One-To-Many Relationship

In the one-to-many relationship a loan is associated with at most
one customer via borrower, a customer is associated with
several (including 0) loans via borrower


Many-To-One Relationships

In a many-to-one relationship a loan is associated with several
(including 0) customers via borrower, a customer is associated
with at most one loan via borrower


Many-To-Many Relationship

A customer is associated with several (possibly 0) loans
via borrower
A loan is associated with several (possibly 0) customers
via borrower


Participation of an Entity Set in a
Relationship Set
Total participation (indicated by double line): every entity in the entity
set participates in at least one relationship in the relationship set
E.g. participation of loan in borrower is total
every loan must have a customer associated to it via borrower
Partial participation: some entities may not participate in any
relationship in the relationship set
E.g. participation of customer in borrower is partial


Alternative Notation for Cardinality
Limits
Cardinality limits can also express participation constraints


Keys

A super key of an entity set is a set of one or more attributes
whose values uniquely determine each entity.
A candidate key of an entity set is a minimal super key
Customer-id is candidate key of customer
account-number is candidate key of account
Although several candidate keys may exist, one of the
candidate keys is selected to be the primary key.


Keys for Relationship Sets

The combination of primary keys of the participating entity sets
forms a super key of a relationship set.
(customer-id, account-number) is the super key of depositor
NOTE: this means a pair of entity sets can have at most one
relationship in a particular relationship set.
E.g. if we wish to track all access-dates to each account by each
customer, we cannot assume a relationship for each access. We
can use a multivalued attribute though
Must consider the mapping cardinality of the relationship set
when deciding the what are the candidate keys
Need to consider semantics of relationship set in selecting the
primary key in case of more than one candidate key


E-R Diagram with a Ternary
Relationship


Cardinality Constraints on Ternary
Relationship
We allow at most one arrow out of a ternary (or greater degree)
relationship to indicate a cardinality constraint
E.g. an arrow from works-on to job indicates each employee works
on at most one job at any branch.
If there is more than one arrow, there are two ways of defining the
meaning.
E.g a ternary relationship R between A, B and C with arrows to B and C
could mean
1. each A entity is associated with a unique entity from B and C or
2. each pair of entities from (A, B) is associated with a unique C entity,
and each pair (A, C) is associated with a unique B
Each alternative has been used in different formalisms
To avoid confusion we outlaw more than one arrow


Binary Vs. Non-Binary Relationships
Some relationships that appear to be non-binary may be better
represented using binary relationships
E.g. A ternary relationship parents, relating a child to his/her father and
mother, is best replaced by two binary relationships, father and mother
Using two binary relationships allows partial information (e.g. only
mother being know)
But there are some relationships that are naturally non-binary
E.g. works-on


Converting Non-Binary Relationships to
Binary Form
In general, any non-binary relationship can be represented using binary
relationships by creating an artificial entity set.
Replace R between entity sets A, B and C by an entity set E, and three
relationship sets:
1. RA, relating E and A 2.RB, relating E and B
3. RC, relating E and C
Create a special identifying attribute for E
Add any attributes of R to E
For each relationship (ai , bi , ci) in R, create
1. a new entity ei in the entity set E 2. add (ei , ai ) to RA
3. add (ei , bi ) to RB 4. add (ei , ci ) to RC


Converting Non-Binary Relationships
(Cont.)
Also need to translate constraints
Translating all constraints may not be possible
There may be instances in the translated schema that
cannot correspond to any instance of R
Exercise: add constraints to the relationships RA, RB and RC to
ensure that a newly created entity corresponds to exactly one entity
in each of entity sets A, B and C
We can avoid creating an identifying attribute by making E a weak
entity set (described shortly) identified by the three relationship sets


Design Issues

Use of entity sets vs. attributes
Choice mainly depends on the structure of the enterprise being
modeled, and on the semantics associated with the attribute in
question.
Use of entity sets vs. relationship sets
Possible guideline is to designate a relationship set to describe an
action that occurs between entities
Binary versus n-ary relationship sets
Although it is possible to replace any nonbinary (n-ary, for n > 2)
relationship set by a number of distinct binary relationship sets, a n-
ary relationship set shows more clearly that several entities
participate in a single relationship.
Placement of relationship attributes


How about doing an ER design
interactively on the board?
Suggest an application to be
modeled.

Weak Entity Sets

An entity set that does not have a primary key is referred to as a
weak entity set.
The existence of a weak entity set depends on the existence of a
identifying entity set
it must relate to the identifying entity set via a total, one-to-many
relationship set from the identifying to the weak entity set
Identifying relationship depicted using a double diamond
The discriminator (or partial key) of a weak entity set is the set of
attributes that distinguishes among all the entities of a weak
entity set.
The primary key of a weak entity set is formed by the primary key
of the strong entity set on which the weak entity set is existence
dependent, plus the weak entity set’s discriminator.


Weak Entity Sets (Cont.)
We depict a weak entity set by double rectangles.
We underline the discriminator of a weak entity set with a
dashed line.
payment-number – discriminator of the payment entity set
Primary key for payment – (loan-number, payment-number)


Weak Entity Sets (Cont.)

Note: the primary key of the strong entity set is not explicitly
stored with the weak entity set, since it is implicit in the
identifying relationship.
If loan-number were explicitly stored, payment could be made a
strong entity, but then the relationship between payment and
loan would be duplicated by an implicit relationship defined by
the attribute loan-number common to payment and loan


More Weak Entity Set Examples

In a university, a course is a strong entity and a course-offering
can be modeled as a weak entity
The discriminator of course-offering would be semester (including
year) and section-number (if there is more than one section)
If we model course-offering as a strong entity we would model
course-number as an attribute.
Then the relationship with course would be implicit in the course-
number attribute


Specialization

Top-down design process; we designate subgroupings within an
entity set that are distinctive from other entities in the set.
These subgroupings become lower-level entity sets that have
attributes or participate in relationships that do not apply to the
higher-level entity set.
Depicted by a triangle component labeled ISA (E.g. customer “is
a” person).
Attribute inheritance – a lower-level entity set inherits all the
attributes and relationship participation of the higher-level entity
set to which it is linked.


Specialization Example


Generalization

A bottom-up design process – combine a number of entity sets
that share the same features into a higher-level entity set.
Specialization and generalization are simple inversions of each
other; they are represented in an E-R diagram in the same way.
The terms specialization and generalization are used
interchangeably.


Specialization and Generalization
(Contd.)
Can have multiple specializations of an entity set based on
different features.
E.g. permanent-employee vs. temporary-employee, in addition to
officer vs. secretary vs. teller
Each particular employee would be
a member of one of permanent-employee or temporary-employee,
and also a member of one of officer, secretary, or teller
The ISA relationship also referred to as superclass - subclass
relationship


Design Constraints on a
Specialization/Generalization
Constraint on which entities can be members of a given
lower-level entity set.
condition-defined
E.g. all customers over 65 years are members of senior-
citizen entity set; senior-citizen ISA person.
user-defined
Constraint on whether or not entities may belong to more than
one lower-level entity set within a single generalization.
Disjoint
an entity can belong to only one lower-level entity set
Noted in E-R diagram by writing disjoint next to the ISA
triangle
Overlapping
an entity can belong to more than one lower-level entity set


Design Constraints on a
Specialization/Generalization
(Contd.)
Completeness constraint -- specifies whether or not an entity in
the higher-level entity set must belong to at least one of the
lower-level entity sets within a generalization.
total : an entity must belong to one of the lower-level entity sets
partial: an entity need not belong to one of the lower-level entity
sets


Aggregation
Consider the ternary relationship works-on, which we saw earlier
Suppose we want to record managers for tasks performed by an
employee at a branch


Aggregation (Cont.)
Relationship sets works-on and manages represent overlapping
information
Every manages relationship corresponds to a works-on relationship
However, some works-on relationships may not correspond to any
manages relationships
So we can’t discard the works-on relationship
Eliminate this redundancy via aggregation
Treat relationship as an abstract entity
Allows relationships between relationships
Abstraction of relationship into new entity
Without introducing redundancy, the following diagram represents:
An employee works on a particular job at a particular branch
An employee, branch, job combination may have an associated manager


E-R Diagram With Aggregation


E-R Design Decisions

The use of an attribute or entity set to represent an object.
Whether a real-world concept is best expressed by an entity set
or a relationship set.
The use of a ternary relationship versus a pair of binary
relationships.
The use of a strong or weak entity set.
The use of specialization/generalization – contributes to
modularity in the design.
The use of aggregation – can treat the aggregate entity set as a
single unit without concern for the details of its internal structure.


E-R Diagram for a Banking
Enterprise


How about doing another ER
design interactively on the board?

Summary of Symbols Used in E-R
Notation


Summary of Symbols (Cont.)


Alternative E-R Notations


UML

UML: Unified Modeling Language
UML has many components to graphically model different
aspects of an entire software system
UML Class Diagrams correspond to E-R Diagram, but several
differences.


Summary of UML Class Diagram Notation


UML Class Diagrams (Contd.)

Entity sets are shown as boxes, and attributes are shown within the
box, rather than as separate ellipses in E-R diagrams.
Binary relationship sets are represented in UML by just drawing a
line connecting the entity sets. The relationship set name is written
adjacent to the line.
The role played by an entity set in a relationship set may also be
specified by writing the role name on the line, adjacent to the entity
set.
The relationship set name may alternatively be written in a box,
along with attributes of the relationship set, and the box is
connected, using a dotted line, to the line depicting the relationship
set.
Non-binary relationships drawn using diamonds, just as in ER
diagrams


UML Class Diagram Notation (Cont.)

overlapping

disjoint

*Note reversal of position in cardinality constraint depiction
*Generalization can use merged or separate arrows independent
of disjoint/overlapping

UML Class Diagrams (Contd.)
Cardinality constraints are specified in the form l..h, where l denotes
the minimum and h the maximum number of relationships an entity
can participate in.
Beware: the positioning of the constraints is exactly the reverse of the
positioning of constraints in E-R diagrams.
The constraint 0..* on the E2 side and 0..1 on the E1 side means that
each E2 entity can participate in at most one relationship, whereas
each E1 entity can participate in many relationships; in other words,
the relationship is many to one from E2 to E1.
Single values, such as 1 or * may be written on edges; The single
value 1 on an edge is treated as equivalent to 1..1, while * is
equivalent to 0..*.


Reduction of an E-R Schema to
Tables

Primary keys allow entity sets and relationship sets to be
expressed uniformly as tables which represent the
contents of the database.
A database which conforms to an E-R diagram can be
represented by a collection of tables.
For each entity set and relationship set there is a unique
table which is assigned the name of the corresponding
entity set or relationship set.
Each table has a number of columns (generally
corresponding to attributes), which have unique names.
Converting an E-R diagram to a table format is the basis
for deriving a relational database design from an E-R
diagram.


Representing Entity Sets as Tables
A strong entity set reduces to a table with the same attributes.


Composite and Multivalued
Attributes
Composite attributes are flattened out by creating a separate attribute
for each component attribute
E.g. given entity set customer with composite attribute name with
component attributes first-name and last-name the table corresponding
to the entity set has two attributes
name.first-name and name.last-name
A multivalued attribute M of an entity E is represented by a separate
table EM
Table EM has attributes corresponding to the primary key of E and an
attribute corresponding to multivalued attribute M
E.g. Multivalued attribute dependent-names of employee is represented
by a table
employee-dependent-names( employee-id, dname)
Each value of the multivalued attribute maps to a separate row of the
table EM
E.g., an employee entity with primary key John and
dependents Johnson and Johndotir maps to two rows:
(John, Johnson) and (John, Johndotir)


Representing Weak Entity Sets
A weak entity set becomes a table that includes a column for
the primary key of the identifying strong entity set


Representing Relationship Sets
as Tables
A many-to-many relationship set is represented as a table with
columns for the primary keys of the two participating entity sets,
and any descriptive attributes of the relationship set.
E.g.: table for relationship set borrower


Redundancy of Tables
Many-to-one and one-to-many relationship sets that are total
on the many-side can be represented by adding an extra
attribute to the many side, containing the primary key of the
one side
E.g.: Instead of creating a table for relationship account-
branch, add an attribute branch to the entity set account


Redundancy of Tables (Cont.)

For one-to-one relationship sets, either side can be chosen to act
as the “many” side
That is, extra attribute can be added to either of the tables
corresponding to the two entity sets
If participation is partial on the many side, replacing a table by an
extra attribute in the relation corresponding to the “many” side
could result in null values
The table corresponding to a relationship set linking a weak
entity set to its identifying strong entity set is redundant.
E.g. The payment table already contains the information that would
appear in the loan-payment table (i.e., the columns loan-number and
payment-number).


Representing Specialization as
Tables
Method 1:
Form a table for the higher level entity
Form a table for each lower level entity set, include primary key of
higher level entity set and local attributes

table table attributes
person name, street, city
customer name, credit-rating
employee name, salary
Drawback: getting information about, e.g., employee requires
accessing two tables


Representing Specialization as
Tables (Cont.)
Method 2:
Form a table for each entity set with all local and inherited
attributes
table table attributes
person name, street, city
customer name, street, city, credit-rating
employee name, street, city, salary

If specialization is total, table for generalized entity (person) not
required to store information
Can be defined as a “view” relation containing union of
specialization tables
But explicit table may still be needed for foreign key constraints
Drawback: street and city may be stored redundantly for persons
who are both customers and employees


Relations Corresponding to
Aggregation

To represent aggregation, create a table containing
primary key of the aggregated relationship,
the primary key of the associated entity set
Any descriptive attributes


Relations Corresponding to
Aggregation (Cont.)
E.g. to represent aggregation manages between relationship
works-on and entity set manager, create a table
manages(employee-id, branch-name, title, manager-name)
Table works-on is redundant provided we are willing to store
null values for attribute manager-name in table manages


E-R Diagram for Exercise 2.10


Existence Dependencies

If the existence of entity x depends on the existence of
entity y, then x is said to be existence dependent on y.
y is a dominant entity (in example below, loan)
x is a subordinate entity (in example below, payment)

loan loan-payment payment

If a loan entity is deleted, then all its associated payment entities
must be deleted also.


Ch2

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