# Database Management Systems

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Database Management System (CS403)
VU
Lecture No. 15
Reading Material
Overview of Lecture
Database and Math Relations
o
Degree and Cardinality of Relation
o
Integrity Constraints
o
Transforming conceptual database design into logical database design
o
Composite and multi-valued Attributes
o
Identifier Dependency
o
In the previous lecture we discussed relational data model, its components and
properties of a table. We also discussed mathematical and database relations. Now we
will discuss the difference in between database and mathematical relations.
Database and Math Relations
We studied six basic properties of tables or database relations. If we compare these
properties with those of mathematical relations then we find out that properties of
both are the same except the one related to order of the columns. The order of
columns in mathematical relations does matter, whereas in database relations it does
not matter. There will not be any change in either math or database relations if we
change the rows or tuples of any relation. It means that the only difference in between
these two is of order of columns or attributes. A math relation is a Cartesian product
of two sets. So if we change the order of theses two sets then the outcome of both will
not be same. Therefore, the math relation changes by changing the order of columns.
For Example , if there is a set A and a set B if we take Cartesian product of A and B
then we take Cartesian product of B and A they will not be equal , so
AxB=BxA
Rests of the properties between them are same.
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Degree of a Relation
We will now discuss the degree of a relation not to be confused with the degree of a
relationship. You would be definitely remembering that the relationship is a link or
association between one or more entity types and we discussed it in E-R data model.
However the degree of a relation is the number of columns in that relation. For
Example consider the table given below:
STUDENT
StID
stName
clName
Sex
S001
Suhail
MCS
M
S002
Shahid
BCS
M
S003
Naila
MCS
F
S004
Rubab
MBA
F
S005
Ehsan
BBA
M
Table 1: The STUDENT table
Now in this example the relation STUDENT has four columns, so this relation has
degree four.
Cardinality of a Relation
The number of rows present in a relation is called as cardinality of that relation. For
example, in STUDENT table above, the number of rows is five, so the cardinality of
the relation is five.
Relation Keys
The concept of key and all different types of keys is applicable to relations as well.
We will now discuss the concept of foreign key in detail, which will be used quite
frequently in the RDM.
Foreign Key
An attribute of a table B that is primary key in another table A is called as foreign key.
For Example, consider the following two tables EMP and DEPT:
EMP (empId, empName, qual, depId)
DEPT (depId, depName, numEmp)
In this example there are two relations; EMP is having record of employees, whereas
DEPT is having record of different departments of an organization. Now in EMP the
primary key is empId, whereas in DEPT the primary key is depId. The depId which is
primary key of DEPT is also present in EMP so this is a foreign key.
Requirements/Constraints of Foreign Key
Following are some requirements / constraints of foreign key:
There can be more than zero, one or multiple foreign keys in a table, depending on
how many tables a particular table is related with. For example in the above example
the EMP table is related with the DEPT table, so there is one foreign key depId,
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whereas DEPT table does not contain any foreign key. Similarly, the EMP table may
also be linked with DESIG table storing designations, in that case EMP will have
another foreign key and alike.
The foreign key attribute, which is present as a primary key in another relation is
called as home relation of foreign key attribute, so in EMP table the depId is foreign
key and its home relation is DEPT.
The foreign key attribute and the one present in another relation as primary key can
have different names, but both must have same domains. In DEPT, EMP example,
both the PK and FK have the same name; they could have been different, it would not
have made any difference however they must have the same domain.
The primary key is represented by underlining with a solid line, whereas foreign key
is underlined by dashed or dotted line.
Primary Key :
Foreign Key :
Integrity Constraints
Integrity constraints are very important and they play a vital role in relational data
model. They are one of the three components of relational data model. These
constraints are basic form of constraints, so basic that they are a part of the data model,
due to this fact every DBMS that is based on the RDM must support them.
Entity Integrity Constraint:
It states that in a relation no attribute of a primary key (PK) can have null value. If a
PK consists of single attribute, this constraint obviously applies on this attribute, so it
cannot have the Null value. However, if a PK consists of multiple attributes, then
none of the attributes of this PK can have the Null value in any of the instances.
Referential Integrity Constraint:
This constraint is applied to foreign keys. Foreign key is an attribute or attribute
combination of a relation that is the primary key of another relation. This constraint
states that if a foreign key exists in a relation, either the foreign key value must match
the primary key value of some tuple in its home relation or the foreign key value must
be completely null.
Significance of Constraints:
By definition a PK is a minimal identifier that is used to identify tuples uniquely. This
means that no subset of the primary key is sufficient to provide unique identification
of tuples. If we were to allow a null value for any part of the primary key, we would
be demonstrating that not all of the attributes are needed to distinguish between tuples,
which would contradict the definition.
Referential integrity constraint plays a vital role in maintaining the correctness,
validity or integrity of the database. This means that when we have to ensure the
proper enforcement of the referential integrity constraint to ensure the consistency and
correctness of database. How? In the DEPT, EMP example above deptId in EMP is
foreign key; this is being used as a link between the two tables. Now in every instance
of EMP table the attribute deptId will have a value, this value will be used to get the
name and other details of the department in which a particular employee works. If the
value of deptId in EMP is Null in a row or tuple, it means this particular row is not
related with any instance of the DEPT. From real-world scenario it means that this
particular employee (whose is being represented by this row/tuple) has not been
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assigned any department or his/her department has not been specified. These were
two possible conditions that are being reflected by a legal value or Null value of the
foreign key attribute. Now consider the situation when referential integrity constrains
is being violated, that is, EMP.deptId contains a value that does not match with any of
the value of DEPT.deptId. In this situation, if we want to know the department of an
employee, then ooops, there is no department with this Id, that means, an employee
has been assigned a department that does not exist in the organization or an illegal
department. A wrong situation, not wanted. This is the significance of the integrity
constraints.
Null Constraints:
A Null value of an attribute means that the value of attribute is not yet given, not
defined yet. It can be assigned or defined later however. Through Null constraint we
can monitor whether an attribute can have Null value or not. This is important and we
have to make careful use of this constraint. This constraint is included in the
definition of a table (or an attribute more precisely). By default a non-key attribute
can have Null value, however, if we declare an attribute as Not Null, then this
attribute must be assigned value while entering a record/tuple into the table containing
that attribute. The question is, how do we apply or when do we apply this constraint,
or why and when, on what basis we declare an attribute Null or Not Null. The answer
is, from the system for which we are developing the database; it is generally an
organizational constraint. For example, in a bank, a potential customer has to fill in a
form that may comprise of many entries, but some of them would be necessary to fill
in, like, the residential address, or the national Id card number. There may be some
entries that may be optional, like fax number. When defining a database system for
such a bank, if we create a CLIENT table then we will declare the must attributes as
Not Null, so that a record cannot be successfully entered into the table until at least
those attributes are not specified.
Default Value:
This constraint means that if we do not give any value to any particular attribute, it
will be given a certain (default) value. This constraint is generally used for the
efficiency purpose in the data entry process. Sometimes an attribute has a certain
value that is assigned to it in most of the cases. For example, while entering data for
the students, one attribute holds the current semester of the student. The value of this
attribute is changed as a students passes through different exams or semesters during
its degree. However, when a student is registered for the first time, it is generally
registered in the first semesters. So in the new records the value of current semester
attribute is generally 1. Rather than expecting the person entering the data to enter 1 in
every record, we can place a default value of 1 for this attribute. So the person can
simply skip the attribute and the attribute will automatically assume its default value.
Domain Constraint:
This is an essential constraint that is applied on every attribute, that is, every attribute
has got a domain. Domain means the possible set of values that an attribute can have.
For example, some attributes may have numeric values, like salary, age, marks etc.
Some attributes may possess text or character values, like, name and address. Yet
some others may have the date type value, like date of birth, joining date. Domain
specification limits an attribute the nature of values that it can have. Domain is
specified by associating a data type to an attribute while defining it. Exact data type
name or specification depends on the particular tool that is being used. Domain helps
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to maintain the integrity of the data by allowing only legal type of values to an
attribute. For example, if the age attribute has been assigned a numeric data type then
it will not be possible to assign a text or date value to it. As a database designer, this is
your job to assign an appropriate data type to an attribute. Another perspective that
needs to be considered is that the value assigned to attributes should be stored
efficiently. That is, domain should not allocate unnecessary large space for the
attribute. For example, age has to be numeric, but then there are different types of
numeric data types supported by different tools that permit different range of values
and hence require different storage space. Some of more frequently supported
numeric data types include Byte, Integer, and Long Integer. Each of these types
supports different range of numeric values and takes 1, 4 or 8 bytes to store. Now, if
we declare the age attribute as Long Integer, it will definitely serve the purpose, but
we will be allocating unnecessarily large space for each attribute. A Byte type would
have been sufficient for this purpose since you won't find students or employees of
age more than 255, the upper limit supported by Byte data type. Rather we can further
restrict the domain of an attribute by applying a check constraint on the attribute. For
example, the age attribute although assigned type Byte, still if a person by mistake
enters the age of a student as 200, if this is year then it is not a legal age from today's
age, yet it is legal from the domain constraint perspective. So we can limit the range
supported by a domain by applying the check constraint by limiting it up to say 30 or
40, whatever is the rule of the organization. At the same time, don't be too sensitive
about storage efficiency, since attribute domains should be large enough to cater the
future enhancement in the possible set of values. So domain should be a bit larger
than that is required today. In short, domain is also a very useful constraint and we
should use it carefully as per the situation and requirements in the organization.
RDM Components
We have up till now studied following two components of the RDM, which are the
Structure and Entity Integrity Constraints. The third part, that is, the Manipulation
Language will be discussed in length in the coming lectures.
Designing Logical Database
Logical data base design is obtained from conceptual database design. We have seen
that initially we studied the whole system through different means. Then we identified
different entities, their attributes and relationship in between them. Then with the help
of E-R data model we achieved an E-R diagram through different tools available in
this model. This model is semantically rich. This is our conceptual database design.
Then as we had to use relational data model so then we came to implementation phase
for designing logical database through relational data model.
The process of converting conceptual database into logical database involves
transformation of E-R data model into relational data model. We have studied both
the data models, now we will see how to perform this transformation.
Transforming Rules
Following are the transforming rules for converting conceptual database into logical
database design:
The rules are straightforward , which means that we just have to follow the rules
mentioned and the required logical database design would be achieved
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There are two ways of transforming first one is manually that is we analyze and
evaluate and then transform. Second is that we have CASE tools available with us
which can automatically convert conceptual database into required logical database
design
If we are using CASE tools for transforming then we must evaluate it as there are
multiple options available and we must make necessary changes if required.
Mapping Entity Types
Following are the rules for mapping entity types:
Each regular entity type (ET) is transformed straightaway into a relation. It means that
whatever entities we had identified they would simply be converted into a relation and
will have the same name of relation as kept earlier.
Primary key of the entity is declared as Primary key of relation and underlined.
Simple attributes of ET are included into the relation
For Example, figure 1 below shows the conversion of a strong entity type into
equivalent relation:
stName
stDoB
stId
STUDENT
STUDENT (stId, stName, stDoB)
Fig. 1: An example strong entity type
Composite Attributes
These are those attributes which are a combination of two or more than two attributes.
For address can be a composite attribute as it can have house no, street no, city code
and country , similarly name can be a combination of first and last names. Now in
relational data model composite attributes are treated differently. Since tables can
contain only atomic values composite attributes need to be represented as a separate
relation
For Example in student entity type there is a composite attribute Address, now in E-R
model it can be represented with simple attributes but here in relational data model,
there is a requirement of another relation like following:
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stName
stDoB
stId
houseNo
STUDENT
streetNo
stAdres
country
areaCode
city
cityCode
STUDENT (stId, stName, stDoB)
STDADRES (stId, hNo, strNo, country, cityCode, city, areaCode)
Fig. 2: Transformation of composite attribute
Figure 2 above presents an example of transforming a composite attribute into RDM,
where it is transformed into a table that is linked with the STUDENT table with the
primary key
Multi-valued Attributes
These are those attributes which can have more than one value against an attribute.
For Example a student can have more than one hobby like riding, reading listening to
music etc. So these attributes are treated differently in relational data model.
Following are the rules for multi-valued attributes:-
An Entity type with a multi-valued attribute is transformed into two relations
One contains the entity type and other simple attributes whereas the second one has
the multi-valued attribute. In this way only single atomic value is stored against every
attribute
The Primary key of the second relation is the primary key of first relation and the
attribute value itself. So in the second relation the primary key is the combination of
two attributes.
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All values are accessed through reference of the primary key that also serves as
stName
stDoB
stId
houseNo
STUDENT
streetNo
stHobby
stAdres
country
areaCode
city
cityCode
STUDENT (stId, stName, stDoB)
STDADRES (stId, hNo, strNo, country, cityCode, city, areaCode)
STHOBBY(stId, stHobby)
Fig. 3: Transformation of multi-valued attribute
foreign key.
Conclusion
In this lecture we have studied the difference between mathematical and database
relations. The concepts of foreign key and especially the integrity constraints are very
important and are basic for every database. Then how a conceptual database is
transformed into logical database and in our case it is relational data model as it is the
most widely used. We have also studied certain transforming rules for converting E-R
data model into relational data model. Some other rule for this transformation will be
studied in the coming lectures
You will receive exercise at the end of this topic.
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