MDA104 Introduction to Databases
3. Relational Model
Vlastislav Dohnal
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Relational Model
Structure of Relational Databases
Conversion of ERD to relational model
(the following is in the next chapters)
Query Language
Fundamental Relational-Algebra-Operations
Additional Relational-Algebra-Operations
Extended Relational-Algebra-Operations
Null Values
Modification of the Database
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Example of a Relation Account
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Attribute Types
Each attribute of a relation has a name
The set of allowed values for each attribute is called the domain of
the attribute
Attribute values are (normally) required to be atomic; that is,
indivisible
E.g., the value of an attribute can be an account number,
but cannot be a set of account numbers
Domain is said to be atomic if all its members are atomic
The special value null is a member of every domain
The null value causes complications in the definition of many
operations
We shall ignore the effect of null values in our main presentation
and consider their effect later
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Relational Model
Formally, given attributes A1, A2, …. An and their domains D1, D2, …. Dn
a relation r is a subset of D1  D2  …  Dn
Thus, a relation is a set of n-tuples (a1, a2, …, an) where each ai  Di
Schema of a relation consists of
a list of attribute definitions
name
type/domain
integrity constraints
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Relation Instance
The current values (relation instance) of a relation are specified by
a table
An element t of r is a tuple
represented by a row in a table
Order of tuples is irrelevant
tuples may be stored in an arbitrary order
Jones
Smith
Curry
Lindsay
customer_name
Main
North
North
Park
customer_street
Harrison
Rye
Rye
Pittsfield
customer_city
customer
attributes
(or columns)
tuples
(or rows)
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Database
A database consists of multiple relations
Information about an enterprise is broken up into parts,
with each relation storing one part of the information
E.g.:
customer : information about customers
account : information about accounts
depositor : which customer owns which account
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The customer Relation
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The Account Relation
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The depositor Relation
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Why Split Information Across Relations?
Storing all information as a single relation such as
bank(account_number, branch_name, balance,
customer_name, customer_street, customer_city)
results in
repetition of information
E.g., if two customers share the same account
What gets repeated?
the need for null values
E.g., to represent a customer without an account
Normalization theory deals with how to design relational schemas
We will study in later…
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Integrity Constraints: Keys
Let K  R, K ≠ , then K is a key.
K is a superkey of R if values for K are sufficient to identify a unique
tuple of each possible relation r(R)
by “possible r ” we mean a relation r that could exist in the
enterprise we are modeling.
Trivial superkey is R.
Example:
Relation
customer ( customer_name, customer_street, customer_city )
Keys: {customer_name, customer_street} and
{customer_name}
are both superkeys, if no two customers can possibly have the
same name.
In real life, an attribute such as customer_id would be used
instead of customer_name
to uniquely identify customers,
but we omit it to keep our examples small, and instead
assume customer names are unique.
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Integrity Constraints: Keys (Cont.)
K is a candidate key if superkey K is minimal.
Example: {customer_name} is a candidate key for Customer,
since it is a superkey and no subset of it is a superkey.
Primary key
a candidate key chosen as the principal means of identifying
tuples within a relation
Should choose an attribute whose value never, or very rarely,
changes.
E.g. email address is unique, but may change
Primary key is depicted in schema using underlined attribute
names.
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Integrity Constraints: Foreign Keys
A relation schema may have an attribute that corresponds to the
primary key of another relation. The attribute is called a foreign key.
Example:
Relations:
customer ( customer_name, customer_street, customer_city )
account ( account_number, branch_name, balance )
depositor ( customer_name, account_number )
Foreign keys:
customer_name and account_number attributes of depositor
are foreign keys to customer and account respectively.
Only values occurring in the primary key attribute of the referenced
relation may occur in the foreign key attribute of the referencing
relation.
A relation may have foreign keys, but it should have a primary key.
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Schema Diagram
Primary keys are emphasized by grey background and
foreign keys by connecting lines.
customer_name
account_number
customer_name
loan_number
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Reduction of ERD to Relational Model
Attributes and primary keys allow entity sets and relationship sets to
be expressed uniformly as relation schemas
These schemas then represent the database schema
For each entity set and relationship set,
there is a unique relation schema.
It is assigned the name of the corresponding entity set or
relationship set.
Each schema has a number of columns
(generally) corresponding to attributes, which have unique names.
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Representing Entity Sets as Schemas
An entity set reduces to a schema with the same attributes.
A strong entity set is handled the same way.
loan ( loan_number, amount )
A weak entity set becomes a table that includes a column for
the primary key of the identifying strong entity set apart its
regular attributes
payment ( loan_number, payment_number,
payment_date, payment_amount )
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Representing Relationship Sets as Schemas
A many-to-many relationship set
is represented as a schema with attributes for the primary
keys of the two participating entity sets,
and any descriptive attributes of the relationship set.
its primary key is formed by the attributes coming from
primary keys of the entity sets.
Example: schema for relationship set borrower
borrower (customer_id, loan_number )
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Representing Relationship Sets (cont.)
A one-to-many relationship set
is represented as a schema in the same way,
But its primary key contains attributes from the primary of
the “many” entity set.
Example: schema for relationship set borrower
borrower (customer_id, loan_number )
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Representing Relationship Sets (cont.)
A one-to-one relationship set
is represented as a schema in the same way,
Its primary key can be the primary of either the entity sets.
i.e., it behaves as in one-to-many
In relational model, this can be handled by adding a unique
constraint
i.e., disallowing the values in the other attributes to repeat.
Example: schema for a one-to-one relationship set borrower
borrower (customer_id, loan_number )
The customer_id can be set unique
independently on the uniqueness of loan_number
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Redundancy of Schemas
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
Example:
Instead of creating a schema for relationship set account_branch
Add an attribute branch_name to the schema arising from entity
set account
branch ( branch_name, branch_city, assets )
account ( account_number, balance, branch_name )
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Redundancy of Schemas (Cont.)
For total one-to-one relationship sets, either side can be chosen to act
as the “many” side
That is, an 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 schema by an extra attribute in the schema
corresponding to the “many” side could result in null values.
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Redundancy of Schemas (Cont.)
The schema corresponding to an identifying relationship set
linking a weak entity set to its strong entity set is redundant.
Example:
The payment schema already contains the attributes that would
appear in the loan_payment schema
i.e., loan_number and payment_number.
Relations
loan ( loan_number, amount )
payment ( loan_number, payment_number,
payment_date, payment_amount )
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Composite Attributes
Composite attributes are flattened out by creating a separate attribute
for each component attribute
Example:
Given entity set customer with a composite attribute name with
component attributes first_name and last_name
The schema corresponding to the entity set has two attributes
name_first_name and name_last_name
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Multivalued Attributes
A multivalued attribute M of an entity E is represented by a separate
schema EM
Schema EM has attributes corresponding to the primary key of E
and an attribute corresponding to the multivalued attribute M
Example:
Multivalued attribute dependent_names of employee is
represented by a schema:
employee_dependent_names =
( employee_id, dependent_name)
Each value of the multivalued attribute maps to a separate tuple of
the relation on schema EM
For example, an employee entity with primary key 123-45-6789
and dependents Jack and Jane maps to two tuples:
(123-45-6789, Jack)
(123-45-6789, Jane)
employee
emploee_id
dependent_names
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Representing Specialization as Schemas
Method 1:
Form a schema for the higherlevel
entity
Form a schema for each lowerlevel
entity set
include primary key of higherlevel
entity set and local
attributes
Schema Attributes
person person_id, name, street, city
customer person_id, credit_rating
employee person_id, salary
Drawback: getting information
about, an employee requires
accessing two relations
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Representing Specialization as Schemas (Cont.)
Method 2:
Form a schema for each entity set with all local and inherited
attributes
If specialization is total, the schema for the generalized entity set
(person) is not required to store information
Can be defined as a “view” relation containing union of
specialization relations
But explicit schema may still be needed for foreign key
constraints
Drawback:
street and city may be stored redundantly for people who are
both customers and employees
Schema Attributes
person person_id, name, street, city
customer person_id, name, street, city, credit_rating
employee person_id, name, street, city, salary
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Schemas Corresponding to Aggregation
Aggregation itself is not represented by any schema, but rather its
corresponding relationship set is used.
To represent a relationship set between an aggregation and an entity
set, create a schema containing
The primary key of the aggregated relationship,
The primary key of the associated entity set, and
Any descriptive attributes
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Schemas Corresponding to Aggregation (Cont.)
Example
employee(employee_id, name)
branch(branch_name, address)
job(title, description)
works_on(employee_id, branch_name, title)
manager(manager_id, name)
To represent relationship manages
between the aggregation works_on and
the entity set manager,
create a schema
manages (employee_id, branch_name, title, manager_id)
Schema works_on is redundant provided we are willing to store null
values for attribute manager_id in relation manages
Summary (Takeaways)
Terminology understanding
Relation (table)
Schema of relation
Database
Schema of database
Integrity constraints
What it does
Primary key, candidate key, super key,
and their mutual relationship
Reduction of ERD to relational model (tables)
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