Lecture 05: Relational Database
Design by ER- & EER-toRelational Mapping
Dr. Dang Tran Khanh
M.eng. Tran Minh Quang
Department of Information Systems
Faculty of Computer Science & Engineering
Outline



Main Phases of Database Design
Conceptual Database Design
Logical Database Design
–


ER- & EER-to-Relational Mapping
Exercises
Reading Suggestion:
–
–
[1]: Chapters 7, 12
[2]: Chapters 15, 16
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
2
Main Phases of Database Design

Three main phases
–
–
–

Conceptual database design
Logical database design
Physical database design
Detailed discussions: see [1] (chapter 12)
–
Six phases
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
3
A simplified diagram to illustrate the main phases of
database design
Main Phases of Database Design

Conceptual database design
–

The process of constructing a model of the data
used in an enterprise, independent of all physical
considerations
Logical database design
–
The process of constructing a model of the data
used in an enterprise based on a specific data
model (e.g. relational), but independent of a
particular DBMS and other physical
considerations
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
5
Main Phases of Database Design

Physical database design
–
The process of producing a description of the
implementation of the database on secondary
storage; it describes the base relations, file
organizations, and indexes design used to
achieve efficient access to the data, and any
associated integrity constraints and security
measures
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
6
Conceptual Database Design
Summarization


Read [1]: chapters 3, 12 for details
To build a conceptual data model of the data
requirements of the enterprise
–
Model comprises entity types, relationship types,
attributes and attribute domains, primary and
alternate keys, structural and integrity constraints
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
7
Conceptual Database Design
Summarization









Step 1: Identify entity types
Step 2: Identify relationship types
Step 3: Identify and associate attributes with entity or
relationship types
Step 4: Determine attribute domains
Step 5: Determine candidate, primary, and alternate key
attributes
Step 6: Consider use of enhanced modeling concepts (optional
step)
Step 7: Check model for redundancy
Step 8: Validate conceptual model against user transactions
Step 9: Review conceptual data model with user
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
8
Conceptual Database Design
Summarization

Step 1: Identify entity types
–

Step 2: Identify relationship types
–

To identify the important relationships that exist between the
entity types
Step 3: Identify and associate attributes with entity or
relationship types
–

To identify the required entity types
To associate attributes with the appropriate entity or
relationship types and document the details of each
attribute
Step 4: Determine attribute domains
–
To determine domains for the attributes in the data model
and document the details of each domain
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
9
Conceptual Database Design
Summarization

Step 5: Determine candidate, primary, and alternate
key attributes
–

Step 6: Consider use of enhanced modeling
concepts (optional step)
–

To identify the candidate key(s) for each entity and if there is
more than one candidate key, to choose one to be the
primary key and the others as alternate keys
To consider the use of enhanced modeling concepts, such
as specialization/generalization, categories (union types)
Step 7: Check model for redundancy
–
To check for the presence of any redundancy in the model
and to remove any that does exist
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
10
Conceptual Database Design
Summarization

Step 8: Validate conceptual model against user
transactions
–

Step 9: Review conceptual data model with user
–

To ensure that the conceptual model supports the required
transactions
To review the conceptual data model with the user to ensure
that the model is a ‘true’ representation of the data
requirements of the enterprise
Check with the previous ERD exercises !!
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
11
A simplified diagram to illustrate the main phases of
database design
Logical Database Design

To translate the conceptual data model into a
logical data model and then to validate this
model to check that it is structurally correct
using normalization and supports the
required transactions
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
13
Logical Database Design

Logical database design for the relational model
–
–
–
–
–
–
–

Step 1: Derive relations for logical data model
Step 2: Validate relations using normalization
Step 3: Validate relations against user transactions
Step 4: Define integrity constraints
Step 5: Review logical data model with user
Step 6: Merge logical data models into global model
(optional step)
Step 7: Check for future growth
ER- & EER-to-Relational Mapping
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
14
The ERD for the COMPANY database
Result of mapping the COMPANY ER schema into a
relational schema
ER- & EER-to-Relational Mapping

ER–
–
–
–
–
–
–

Step 1: Mapping of Regular Entity Types
Step 2: Mapping of Weak Entity Types
Step 3: Mapping of Binary 1:1 Relationship Types
Step 4: Mapping of Binary 1:N Relationship Types
Step 5: Mapping of Binary M:N Relationship Types
Step 6: Mapping of Multivalued attributes
Step 7: Mapping of N-ary Relationship Types
EER–
–
Step 8: Options for Mapping Specialization or Generalization.
Step 9: Mapping of Union Types (Categories)
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
17
ER-to-Relational Mapping

Step 1: Mapping of Regular (strong) Entity Types
–
–
–
–
Entity --> Relation
Attribute of entity --> Attribute of relation
Primary key of entity --> Primary key of relation
Example: We create the relations EMPLOYEE,
DEPARTMENT, and PROJECT in the relational schema
corresponding to the regular entities in the ER diagram.
SSN, DNUMBER, and PNUMBER are the primary keys for
the relations EMPLOYEE, DEPARTMENT, and PROJECT
as shown
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
18
The ERD for the COMPANY database
Strong Entity
Types
ER-to-Relational Mapping

Step 2: Mapping of Weak Entity Types
–
–
–
–
–
For each weak entity type W in the ER schema with owner entity type E,
create a relation R and include all simple attributes (or simple components
of composite attributes) of W as attributes of R
In addition, include as foreign key attributes of R the primary key
attribute(s) of the relation(s) that correspond to the owner entity type(s)
The primary key of R is the combination of the primary key(s) of the
owner(s) and the partial key of the weak entity type W, if any
Example: Create the relation DEPENDENT in this step to correspond to
the weak entity type DEPENDENT. Include the primary key SSN of the
EMPLOYEE relation as a foreign key attribute of DEPENDENT (renamed
to ESSN)
The primary key of the DEPENDENT relation is the combination {ESSN,
DEPENDENT_NAME} because DEPENDENT_NAME is the partial key of
DEPENDENT
Note: CASCADE option as implemented
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
20
The ERD for the COMPANY database
Owner’s PK
PK
Weak Entity
Types
Partial key
Result of mapping the COMPANY ER schema into a
relational schema
ER-to-Relational Mapping

ER–
–
–
–
–
–
–

Step 1: Mapping of Regular Entity Types
Step 2: Mapping of Weak Entity Types
Step 3: Mapping of Binary 1:1 Relationship Types
Step 4: Mapping of Binary 1:N Relationship Types
Step 5: Mapping of Binary M:N Relationship Types
Step 6: Mapping of Multivalued attributes
Step 7: Mapping of N-ary Relationship Types
Transformation of binary relationships - depends on
functionality of relationship and membership class of
participating entity types
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
23
ER-to-Relational Mapping

Mandatory membership class
–
–
–
For two entity types E1 and E2: If E2 is a mandatory
member of an N:1 (or 1:1) relationship with E1, then the
relation for E2 will include the prime attributes of E1 as a
foreign key to represent the relationship
For a 1:1 relationship: If the membership class for E1 and
E2 are both mandatory, a foreign key can be used in either
relation
For an N:1 relationship: If the membership class of E2,
which is at the N-side of the relationship, is optional (i.e.
partial), then the above guideline is not applicable
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
24
ER-to-Relational Mapping
DEPARTMENT

1
OFFER
MODULE
N
Assume every module must be offered by a
department, then the entity type MODULE is a
mandatory member of the relationship OFFER. The
relation for MODULE is:
MODULE(MDL-NUMBER, TITLE, TERM, ..., DNAME)
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
25
The ERD for the COMPANY database
N:1
Relationships
Result of mapping the COMPANY ER schema into a
relational schema
ER-to-Relational Mapping

Optional membership classes
–
–
If entity type E2 is an optional member of the N:1
relationship with entity type E1 (i.e. E2 is at the N-side of
the relationship), then the relationship is usually
represented by a new relation containing the prime
attributes of E1 and E2, together with any attributes of the
relationship. The key of the entity type at the N-side (i.e. E2)
will become the key of the new relation
If both entity types in a 1:1 relationship have the optional
membership, a new relation is created which contains the
prime attributes of both entity types, together with any
attributes of the relationship. The prime attribute(s) of either
entity type will be the key of the new relation
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
28
ER-to-Relational Mapping
BORROWER

1
ON_LOAN
N
BOOK
One possible representation of the relationship:
BORROWER(BNUMBER, NAME, ADDRESS, ...)
BOOK(ISBN, TITLE, ..., BNUMBER)

A better alternative:
BORROWER(BNUMBER, NAME, ADDRESS, ...)
BOOK(ISBN, TITLE, ...)
ON_LOAN(ISBN, BNUMBER)
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
29
The ERD for the COMPANY database
1:N (both optional)
Result of mapping the COMPANY ER schema into a
relational schema
???
[1]: Step 4, p. 195,
chapter 7
ER-to-Relational Mapping

N:M binary relationships:
–
–

An N:M relationship is always represented by a new relation
which consists of the prime attributes of both participating
entity types together with any attributes of the relationship
The combination of the prime attributes will form the primary
key of the new relation
Example: ENROL is an M:N relationship between
STUDENT and MODULE. To represent the
relationship, we have a new relation:
ENROL(SNUMBER, MDL-NUMBER, DATE)
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
32
The ERD for the COMPANY database
M:N
Result of mapping the COMPANY ER schema into a
relational schema
ER-to-Relational Mapping

ER–
–
–
–
–
–
–
Step 1: Mapping of Regular Entity Types
Step 2: Mapping of Weak Entity Types
Step 3: Mapping of Binary 1:1 Relationship Types
Step 4: Mapping of Binary 1:N Relationship Types
Step 5: Mapping of Binary M:N Relationship
Types
Step 6: Mapping of Multivalued attributes
Step 7: Mapping of N-ary Relationship Types
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
35
ER-to-Relational Mapping

Transformation of recursive/involuted relationships
–
–
Relationship among different instances of the same entity
The name(s) of the prime attribute(s) needs to be changed
to reflect the role each entity plays in the relationship
1
MARRY
PERSON
M
1
COMPRISE
PART
N
SUPERVISE
EMPLOYEE
1
N
ER-to-Relational Mapping

Example 1: 1:1 involuted relationship, in
which the memberships for both entities are
optional
PERSON(ID, NAME, ADDRESS, ...)
MARRY(HUSBAND-ID, WIFE_ID, DATE_OF_MARRIAGE)
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
37
ER-to-Relational Mapping

Example 2: 1:M involuted relationship.
–
–

If the relationship is mandatory or almost mandatory:
EMPLOYEE(ID, ENAME, ..., SUPERVISOR_ID)
If the relationship is optional:
EMPLOYEE(ID, ENAME, ...)
SUPERVISE(ID, START_DATE, ..., SUPERVISOR_ID)
Example 3: N:M involuted relationship
PART(PNUMBER, DESCRIPTION, ...)
COMPRISE( MAJOR-PNUMBER, MINOR-PNUMBER, QUANTITY)
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
38
ER- & EER-to-Relational Mapping

ER–
–
–
–
–
–
–

Step 1: Mapping of Regular Entity Types
Step 2: Mapping of Weak Entity Types
Step 3: Mapping of Binary 1:1 Relationship Types
Step 4: Mapping of Binary 1:N Relationship Types
Step 5: Mapping of Binary M:N Relationship Types
Step 6: Mapping of Multivalued attributes
Step 7: Mapping of N-ary Relationship Types
EER–
–
Step 8: Options for Mapping Specialization or Generalization.
Step 9: Mapping of Union Types (Categories)
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
39
ER-to-Relational Mapping

Step 6: Mapping of Multivalued attributes
–
–
For each multivalued attribute A, create a new relation R. This
relation R will include an attribute corresponding to A, plus the
primary key attribute K-as a foreign key in R-of the relation that
represents the entity type or relationship type that has A as an
attribute
The primary key of R is the combination of A and K. If the
multivalued attribute is composite, we include its simple
components
Example: The relation DEPT_LOCATIONS is created. The
attribute DLOCATION represents the multivalued attribute
LOCATIONS of DEPARTMENT, while DNUMBER-as foreign keyrepresents the primary key of the DEPARTMENT relation. The
primary key of R is the combination of {DNUMBER, DLOCATION}
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
40
The ERD for the COMPANY database
Multivalued Attr.
Result of mapping the COMPANY ER schema into a
relational schema
ER-to-Relational Mapping

Step 7: Mapping of N-ary Relationship Types
–
–
–
For each n-ary relationship type R, where n>2, create a new
relationship S to represent R
Include as foreign key attributes in S the primary keys of the
relations that represent the participating entity types
Also include any simple attributes of the n-ary relationship
type (or simple components of composite attributes) as
attributes of S
Example: The relationship type SUPPY in the ER below. This can
be mapped to the relation SUPPLY shown in the relational
schema, whose primary key is the combination of the three foreign
keys {SNAME, PARTNO, PROJNAME}
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
43
ER-to-Relational Mapping
FIGURE 4.11 Ternary relationship types
(a) The SUPPLY relationship
Note: if the cardinality
constraint on any of the entity
types E participating in the
relationship is 1, the PK
should not include the FK
attributes that reference the
relation E’ corresponding to E
(see section 4.7 [1])
ER-to-Relational Mapping
Summary of Mapping Constructs & Constraints
Correspondence between ER and Relational Models
ER Model
Entity type
1:1 or 1:N relationship type
M:N relationship type
n-ary relationship type
Simple attribute
Composite attribute
Multivalued attribute
Value set
Relational Model
“Entity” relation
Foreign key (or “relationship” relation)
“Relationship” relation and two foreign keys
“Relationship” relation and n foreign keys
Attribute
Set of simple component attributes
Relation and foreign key
Domain
Key attribute
Primary (or secondary) key
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
45
ER- & EER-to-Relational Mapping

ER–
–
–
–
–
–
–

Step 1: Mapping of Regular Entity Types
Step 2: Mapping of Weak Entity Types
Step 3: Mapping of Binary 1:1 Relationship Types
Step 4: Mapping of Binary 1:N Relationship Types
Step 5: Mapping of Binary M:N Relationship Types
Step 6: Mapping of Multivalued attributes
Step 7: Mapping of N-ary Relationship Types
EER–
–
Step 8: Options for Mapping Specialization or Generalization.
Step 9: Mapping of Union Types (Categories)
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
46
EER-to-Relational Mapping

Step8: Options for Mapping Specialization or Generalization.
Convert each specialization with m subclasses {S1, S2,….,Sm} and generalized
superclass C, where the attributes of C are {k,a1,…an} and k is the (primary)
key, into relational schemas using one of the four following options:
Option 8A: Multiple relations-Superclass and subclasses.
Create a relation L for C with attributes Attrs(L) = {k,a1,…an} and PK(L) = k. Create a relation
Li for each subclass Si, 1 <= i <= m, with the attributesAttrs(Li) = {k} U {attributes of Si} and
PK(Li)=k. This option works for any specialization (total or partial, disjoint of over-lapping).
Option 8B: Multiple relations-Subclass relations only
Create a relation Li for each subclass Si, 1 <= i <= m, with the attributes Attr(Li) = {attributes
of Si} U {k,a1…,an} and PK(Li) = k. This option only works for a specialization whose
subclasses are total (every entity in the superclass must belong to (at least) one of the
subclasses)
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
47
EER-to-Relational Mapping
Option 8C: Single relation with one type attribute
Create a single relation L with attributes Attrs(L) = {k,a1,…an} U
{attributes of S1} U…U {attributes of Sm} U {t} and PK(L) = k. The
attribute t is called a type (or discriminating) attribute that indicates
the subclass to which each tuple belongs
Option 8D: Single relation with multiple type attributes
Create a single relation schema L with attributes Attrs(L) = {k,a1,…an} U
{attributes of S1} U…U {attributes of Sm} U {t1, t2,…,tm} and PK(L) = k.
Each ti, 1 <= i <= m, is a Boolean type attribute indicating whether a
tuple belongs to the subclass Si
Option 8A is preferred !!
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
48
Example: Option 8A
Example: Option 8B
Tonnage
Example: Option 8C
EngType
Serving as the type attribute
Example: Option 8D
Boolean type attributes
EER-to-Relational Mapping

Mapping of Shared Subclasses (Multiple
Inheritance)
–
–
A shared subclass, such as STUDENT_ASSISTANT, is a
subclass of several classes, indicating multiple inheritance.
These classes must all have the same key attribute;
otherwise, the shared subclass would be modeled as a
category.
We can apply any of the options discussed in Step 8 to a
shared subclass, subject to the restriction discussed in Step
8 of the mapping algorithm. Below both 8C and 8D are used
for the shared class STUDENT_ASSISTANT
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
53
Example: Mapping of
Shared Subclasses
Example: Mapping of
Shared Subclasses
Course
Major
EER-to-Relational Mapping

Step 9: Mapping of Union Types (Categories).
–
–
–
For mapping a category whose defining superclasses have
different keys, it is customary to specify a new key attribute, called
a surrogate key, when creating a relation to correspond to the
category.
In the example below we can create a relation OWNER to
correspond to the OWNER category and include any attributes of
the category in this relation. The primary key of the OWNER
relation is the surrogate key, which we called OwnerId
We also include the surrogate key attribute OwnerId as FK in each
relation corresponding to a superclass of the category in order to
specify the correspondence in values between the surrogate key
and the PK of each superclass
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
56
Example
OwnerId
CYear
Exercises (in-class)
Map the above ERD into relational schemas.
Justify your choice of mapping options.
Summary



3 Main Phases of Database Design: An Overview
Conceptual Database Design: A Summarization
Logical Database Design
–



ER- & EER-to-Relational Mapping
Exercises & homework
Reading Suggestion & homework: do not forget !!
Next Lecture: (students’ presentation)
–
–
Relational Algebra & Relational Calculus
[1]: Chapter 6
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
59
Exercises

Homework:
–
–
[1]: Exercise 7.5, p. 204
Map all ERDs of the previous exercises to
corresponding relational database schemas
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
60
Exercises

Homework:
Give a database scheme of a
company as
customer(C-Id, name, addr, city)
– product(P-Id, name, unit, description)
– buying(C-id, P-id, date, quantity, price)
– selling(C-id, P-id, date, quantity, price)
Answer following questions using SQL
–
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
61
Exercises

Homework:
1.
2.
3.
4.
5.
6.
Display all customers
Display all customers but the information to be displayed
are customer id and customer name only
Similar to question 2 but customers to be selected are in
HCM city only
Display all the products sold on 10/03/2007
Display all the customers who supplied product P01 on
10/03/2007
Similar to question 5 but the information to be displayed
includes C-id, C-name, P-id, P-name.
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
62
Exercises

Homework:
7. Display customers who buy the products supplied by
customer whose name is “Intel”
8. Display product which are concurrently bought and sold
on 10/03/2007
9. Display customers who paid the greatest amount of
money for buying product on 10/03/2007
10. Display customers who got the greatest amount of
money by selling product to the company in the year
2006
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
63
Q&A
Dr. Dang Tran Khanh (dtkhanh@hcmut.edu.vn), M.eng. Tran Minh Quang (quangtran@cse.hcmut.edu.vn)
64