Instructor: Churee Techawut Basic Concepts of Relational Database Chapter 5 CS (204)321 Database...

Instructor: Churee Techawut

Basic Concepts of Relational Database

Chapter 5

CS (204)321 Database System I

Outlines

1) Relational Database

2) Relational Data Model

3) Relational Database Constraints and Relational Database Schemas

4) Update Operations on Relations

5) Relational Algebra

Relational Database

Definition (by C.J. Date)

“ A relational database is a database that is perceived by its users as a collection of tables. It is not just a database in which the data is physically stored as tables. ”

Note: Relation is a mathematical term for a table.

Relational Data Model

The relational model of data is based on the concept of a Relation. A relation is a mathematical concept based on the ideas of sets.

The strength of the relational approach to data management comes from the formal foundation provided by the theory of relations.

We review the essentials of the relational approach in this chapter.

Concepts


RELATION: A table of values

What is “Relation” ?

Each column typically is called by its column name or column header or attribute name.

Sometimes row-ids or sequential numbers are assigned to identify the rows in the table.

Each row has a value of an item or set of items that uniquely identifies that row in the table.

Each row represents a fact that corresponds to a real-world entity or relationship.

A relation may alternately be thought of as a set of columns.

A relation may be thought of as a set of rows.


A relation is a named, 2-dimentional table of data. Not all tables qualify as relation.

Relation properties

Every relation has a unique name.

Each column has a unique name.

No 2 rows are identical.

Ordering of rows is not significant.

Ordering of columns is not significant.

All attribute values are atomic. (There always exists precisely one value, never a set of values)

Column values are of the same kind.


For Example:

CUSTOMER (Cust-id, Cust-name, Address, Phone#)

Relation schema

R (A1, A2, .....An)

R is the name of relation.Degree of relation is the numbers of attributes of its relation schema.

Relation schema R is defined over attributes A1, A2, .....An

CUSTOMER is a relation defined over the four attributes Cust-id, Cust-name, Address, Phone#, each of which has a domain or a set of valid values.

Degree of relation is 4.


For Example:

Cust-id : The set of valid 6-digit numbers. Cust-name : The set of customer names. Address : The set of home address where customers live. Phone# : The set of 10-digit phone numbers valid in Thailand.

Domain

“ A domain D is a set of atomic values, all of the same type. ”

All values in a column come from the same domain.


A domain has a logical definition.e.g., “USA_phone_numbers” are the set of 10 digit phone numbers valid in the U.S.

A domain may have a data-type or a format defined for it. e.g., The USA_phone_numbers may have a format: (ddd)-ddd-dddd where each d is a decimal digit. e.g., Dates have various formats such as monthname, date, year or yyyy-mm-dd, or dd mm,yyyy etc.

An attribute designates the role played by the domain. e.g., The domain Date may be used to define attributes “Invoice-date” and “Payment-date”.

Domain (Continued)


Each attribute in the model should be assigned domain information which includes:

- Data type- Length- Data format (e.g., Date format is dd/mm/yy)- Range- Constraints (special restrictions on allowable values)- Null support- Default value (if any)

Domain (Continued)


A relation instance, r , of the relation schema

Relation instance

R (A1, A2, .....An),

denoted by r(R) is a mathematical relation of degree n on the domains dom(A1), dom(A2),…, dom(An), which is the subset of the Cartesian Product of the domains that define R.

))(...)()(()( 21 nAdomAdomAdomRr

R is also called the intension of a relation.

r is also called the extension of a relation.


A tuple is an ordered set of values.

Tuple

Columns in a table are also called attributes of the relation.

A relation may be regarded as a set of tuples (rows).

<632895, "John Smith", "101 Main St. Atlanta, GA 30332", "(404) 894-2000"> is a tuple belonging to the CUSTOMER relation.

Each row in the CUSTOMER table may be referred to as a tuple in the table and would consist of four values.

Each value is derived from an appropriate domain.


We refer to component values of a tuple t

by t[Ai] = vi (the value of attribute Ai for tuple t).

Similarly, t[Au, Av, ..., Aw] refers to the subtuple of t containing the values of attributes Au, Av, ..., Aw, respectively.

Tuple (Continued)


Let S1 = {0,1}

Let S2 = {a,b,c}

Let 21 SSR

Then for example: },1,,0,,0{)( cbaRr

is one possible ‘state’ or ‘population’ or ‘extension’ r of the relation R, defined over domains S1 and S2. It has three tuples.


Terminology

Formal Terms Informal Terms

Relation Table

Attribute/Domain Column

Tuple Row

Domain Values in a column or pool of legal values

Schema of a relation Table definition

Extension Populated table

Degree No. of columns

Cardinality No. of rows

Primary key Unique identifier


Example


Key fields

Keys are special fields that serve two main purposes:

- Primary keys are unique identifiers of the relation. Examples can use SSN as a primary key. This is how we can guarantee that all rows are unique.

- Foreign key is a column or columns whose values are the same as a primary key of another table.

Keys can be simple (a single field) or composite (more than one field)

Keys usually are used as indexes to speed up the response to user queries.

Relational Constraints

There are three main types of constraints:

“ Constraints are conditions that must hold on all valid relation instances. ” (Elmasri&Navathe, 2000)

Key constraints

Entity integrity constraints

Referential integrity constraints

What are relational constraints?

“ Restrictions on data that can be specified on a relational database schema. ” (Date, 2000)


Key constraints

Superkey of R: A set of attributes SK of R such that no two tuples in any valid relation instance r(R) will have the same value for SK. That is, for any distinct tuples t1 and t2 in r(R), t1[SK] t2[SK].

Key of R: A "minimal" superkey; that is, a superkey K such that removal of any attribute from K results in a set of attributes that is not a superkey.

Example: The CAR relation schema:CAR(State, Reg#, SerialNo, Make, Model, Year)

has two keys Key1 = {State, Reg#}, Key2 = {SerialNo}, which are also superkeys. {SerialNo, Make} is a superkey but not a key.


Key constraints (Continued)

The CAR relation with two candidate keys: LicenseNumber and EngineSerialNumber.


Key constraints (Continued)

A relation schema may have more than 1 key. Each of the keys is called a candidate key. One of the candidate keys are designated as the primary key of the relation.

If a relation has several candidate keys, one is chosen arbitrarily to be the primary key. The primary key attributes are underlined.


Entity integrity constraints

Relational Database Schema: A set S of relation schemas that belong to the same database. S is the name of the database. S = {R1, R2, ..., Rn}

Entity Integrity: The primary key attributes PK of each relation schema R in S cannot have null values in any tuple of r(R). This is because primary key values are used to identify the individual tuples. t[PK] null for any tuple t in r(R)

Note: Other attributes of R may be similarly constrained to disallow null values, even though they are not members of the primary key.


Entity integrity constraints (Continued)

A Null is created by making no entry at all, so a null denotes the absence of a value.

- The value does not exist

- The value exists, but it is not known.

- The value is unknown, or it is not applicable.

A null can have any of the following meanings:


Referential integrity constraints

A constraint involving two relations (the previous constraints involve a single relation).

Used to specify a relationship among tuples in two relations: the referencing relation and the referenced relation.

Tuples in the referencing relation R1 have attributes FK (called foreign key attributes) that reference the primary key attributes PK of the referenced relation R2. A tuple t1 in R1 is said to reference a tuple t2 in R2 if t1[FK] = t2[PK].

A referential integrity constraint can be displayed in a relational database schema as a directed arc from R1. FK to R2.


Referential integrity constraints (Continued)

Statement of the constraintThe value in the foreign key column (or columns) FK of the the referencing relation R1 can be either:

(1) a value of an existing primary key value of the corresponding primary key PK in the referenced relation R2, or..

(2) a null.

In case (2), the FK in R1 should not be a part of its own primary key.


Referential integrity constraints displayed on the COMPANY relational database schema


Key constraints (columns)

Entity integrity constraints (rows)

Referential integrity constraints(between tables)

Summary of relational constraints

Update Operations on Relations

UPDATE operations consist of:

INSERT a tuple

DELETE a tuple

MODIFY a tuple

Integrity constraints should not be violated by the update operations. Several update operations may have to be grouped together.

Updates may propagate to cause other updates automatically. This may be necessary to maintain integrity constraints.


In case of integrity violation, several actions can be taken:

Cancel the operation that causes the violation (REJECT option)

Perform the operation but inform the user of the violation

Trigger additional updates so the violation is corrected (CASCADE option, SET NULL option)

Execute a user-specified error-correction routine

e


Insert operation

Insert <‘Cecilia’, ‘F’, ‘Kolonsky’, null, ‘1960-04-05’, ‘6357 Windy Lane, Katy, TX’, F, 28000, null, 4> into EMPLOYEE.

This insertion violates the entity integrity constraint (null for the primary key SSN), so it is rejected.

Insert <‘Cecilia’, ‘F’, ‘Kolonsky’, ‘677678989’, ‘1960-04-05’, ‘6357 Windy Lane, Katy, TX’, F, 28000, null, 4> into EMPLOYEE.

This insertion satisfies all constraints, so it is acceptable.


Delete operation

Delete the WORKS_ON tuple with ESSN = ‘999887777’ and PNO = 10.

This deletion is acceptable.

Delete the EMPLOYEE tuple with SSN = ‘999887777’

This deletion is not acceptable, because tuples in WORKS_ON refer to this tuple. Hence, if the tuple is deleted, referential integrity violations will result.


Modify/Update operation

Update the SALARY of the EMPLOYEE tuple with SSN = ‘999887777’ to 28000.

This update is acceptable.

Update the SSN of the EMPLOYEE tuple with SSN = ‘999887777’ to ‘987654321’.

This update is unacceptable, because it violates primary key and referential integrity constraints.

Relational Algebra

Relational algebra is a set of operations to manipulate data and enable the user to specify basic retrieval requests.

The result of a retrieval is a new relation, which may have been formed from one or more relations.

Three groups of relational algebra operations:

Unary relational operations

Binary relational operations

Set theoretic operations

Relational Algebra

Unary relational operations:

The SELECT operation

The PROJECT operation

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Instructor: Churee Techawut Basic Concepts of Relational Database Chapter 5 CS (204)321 Database...

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