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The Relational Data Model
David J. Stucki
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Relational Model Concepts
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Fundamental concept: the relation
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The Relational Model represents an entire database
as a collection of relations
Idea of a relation: A table of values
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Each row is some collection of facts about an entity
Each column is a single attribute about the entities in the table
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Relational Model Concepts
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Tuple – one row of a relation
Attribute – one column of a relation
Relation – the whole table
Domain of an Attribute – all the values that attribute can have
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Domain
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All the possible values an attribute can take
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Atomic
Remember your mathematics?
Example domains:
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US Phone Numbers: the set of all 10-digit phone numbers
Local Phone Numbers: the set of all 7-digit phone numbers
Social Security Numbers: the set of all 9-digit numbers
Names: the set of all possible names
GPAs: the set of all possible values between 0.0 and 4.0
Data type: a format for a domain
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US Phone Numbers: (ddd)ddd-dddd
GPAs: any real-valued number
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Relation Schema
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Denoted by R(A1, A2, ...,An)
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Consists of a relation name and a list of attributes
Description of what the relation should contain
STUDENT relation:
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STUDENT(Name, SSN, Address, GPA)
Can also include data type:
STUDENT(Name:String, SSN:Social_Security_Nums,
Address: String, GPA: Real)
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Degree (or arity) of a relation
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Number of attributes n of its relation schema
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Relation
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A particular set of tuples for a given relation
schema (also known as a relation state)
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Set of n-tuples r = {t1, t2, ..., tm}
The “state” of the relation is its current configuration (i.e.
current contents)
Each tuple in the set is an ordered list of values
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Each element of the tuple corresponds to a particular attribute
for the relation
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Characteristics of Relations
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Ordering of tuples
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Uniqueness of tuples
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No duplicate tuples in a relation!
Unknown values
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Relation is a set
Sets have no order
Relation is not sensitive to ordering of tuples
NULL value – used when value can’t be known or does not exist
Interpretation
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Relation is an assertion of facts
Each tuple can be thought of as a fact about the world
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Or as a predicate in first order logic
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Characteristics of Relations
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Order of attributes and values is not that
important
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Alternative definition of a relation
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As long as correspondence between attributes and values
maintained
Tuple considered as a set of (<attribute>, <value>) pairs
Each pair gives the value of the mapping from an attribute Ai to a
value vi from dom(Ai)
Use the first definition of relation
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Attributes and the values within tuples are ordered
Simpler notation
But alternative has application in later formalisms
Characteristics of Relations
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Values in tuples
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Each value in a tuple is atomic
Flat relational model
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Multivalued attributes
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Composite and multivalued attributes not allowed
First normal form assumption
Must be represented by separate relations
Composite attributes
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Represented only by simple component attributes in basic
relational model
Relational Model Constraints
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A constraint is a restriction on the values in a
database state
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Implicit constraints (model-based constraints)
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Inherent in the data model itself
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Explicit constraints (schema-based constraints)
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E.g. no duplicate tuples in a relation
Can be explicitly enforced/expressed in the schema
Application-based constraints (business rules)
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Derived from miniworld represented by database
Cannot be explicitly enforced by the schema
Must be enforced by application programs themselves
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Schema-based constraints
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Domain constraints
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Data type constraint
Each attribute in a tuple may only take on a value from
the domain of that attribute
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Schema-based constraints
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Key constraints
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Remember – each tuple in a relation must be unique
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No duplicate tuples!
This means that no two tuples have the same combination of
attributes for all of their attributes
Usually there is a subset of attributes that control
uniqueness
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We call this subset a superkey
Definition: Let SK be a subset of attributes of the relation R
that form a superkey. Then for any two distinct tuples t1 and
t2 in a relation state r of R:
t1[SK] != t2[SK]
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Schema-based constraints
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Superkeys can have redundant attributes
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Ex: {First Name, Last Name, SSN} could be a superkey
Don’t really need First Name and Last Name to be unique –
SSN is guaranteed to be unique
keys
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A key is a minimal superkey
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Remove one attribute from a key and it is no longer a superkey!
A key is always a superkey, but not all superkeys are keys
There can be more than one key in a relation
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Ex: {SSN} {Student ID}
Common to identify one of these keys as as a primary key
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Primary key uniquely identifies tuples in a relation to other
relations and outside applications
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Schema-based constraints
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Constraints can apply not just to single relations
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Relational Database Schema
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We need to be able to talk about constraints that cross
relations
More Terminology!
Set of relation schemas S = {R1, R2, ..., Rm}
Set of integrity constraints IC
Relational Database State
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Set of relation states for a relational database such
that all integrity constraints are satisfied
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Invalid state – state that violates an integrity constraint
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Schema-based constraints
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Entity integrity constraint
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No primary key can have a NULL value
Remember – primary key uniquely identifies a tuple!
Referential integrity constraint
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Specified between two relations
A tuple in one relation that refers to a tuple in a
second relation MUST refer to an existing tuple
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You can’t put in “placeholder” references – every reference
must be resolvable when you make the reference
Uses the concept of a foreign key
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Schema-based constraints
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Where do referential integrity constraints come from?
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Connections in the data
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Other constraints
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Semantic integrity constraints
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Constraints that come from outside the basic
relationships between tuples
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“Business rules”
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“no employee can have a salary larger than their supervisor”
“no employee can log more than 60 hours of time in a week”
Usually modeled at the application level, but
sometimes can be modeled in the database
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“Triggers” – “when event X occurs perform action Y”
“Assertions” – “make sure that no matter what action X does,
condition Y is always true”
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Operations
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The relational model has two types of
operations:
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Retrievals
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Getting information out of the database
Updates
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Adding/changing information in the database
Different kinds of updates:
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INSERT
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Add new tuple to a relation
DELETE
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Remove a tuple from a relation
UPDATE
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Change an attribute value in a tuple in a relation
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Updates & Constraints
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The DBMS must make sure that updates are not
allowed to violate integrity constraints
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Check to make sure that attributes in an INSERT do
not violate constraints
DELETE can cause referential constraint violations
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Removing a tuple being referred to by another tuple
UPDATE can cause referential constraint violations
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Changing a primary key can cause all sorts of referential
problems for any tuple referring to the updated tuple
Changing a foreign key can only happen if the tuple the
foreign key refers to already exists
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ER-Relational Mapping
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ER-Model to Relational Model
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Once we have our ER-Model, we use it to come
up with our Relational model
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Must map elements of ER-model to elements of
relational model
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Entities, Relationships, Attributes, etc. must become
Relations, Attributes, etc.
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Strong Entity Types
Each strong entity type in an ER model becomes
a relation
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Entity type E -> Relation R
Simple attributes of E become attributes of R
Include only the component attributes of a composite
attribute
Choose one key of E to become the primary key of R
Fname
M
Lname
EMPLOYEE
Ssn
Ssn
Name
EMPLOYEE
Fname
M
Lname
Address
Address
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Weak Entity Types
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Each weak entity type becomes a relation
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Weak entity W owned by entity E
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Entity E -> Relation R1
Entity W -> Relation R2
All simple attributes of W become attributes in R2
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Include as a foreign key the primary key attribute of R1
Primary key of R2 will be that foreign key, plus the partial key
of W
EMPLOYEE
Ssn
1
EMPLOYEE
Fname
M
Lname
Address
Dependents_of
DEPENDENT
N
Sex
Essn
Name
Sex
Bdate
Relationship
DEPENDENT
Bdate
Name
Relationship
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Binary 1:1 Relationships
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Three approaches:
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Foreign Key Approach
Merged relation Approach
Cross-reference Approach
Should use “Foreign key approach” unless there is
good reason not to
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Binary 1:1 Relationships
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Foreign key approach
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Two entities in the relationship – E1 and E2
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Generate two relations R1 and R2 associated with E1 and E2
Include in R1 a foreign key pointing at the primary key of R2
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R1 should be an entity with Total Participation if possible
EMPLOYEE
Ssn
Fname
M
Lname
Address
DEPARTMENT
Dname
Dnumber
MgrSsn
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Binary 1:1 relationships
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Merged relation approach
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If both entities have TOTAL participation in the
relationship, you can merge them into a single entity
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Each table would have an exact one-to-one correspondence
between rows, so they’re essentially the same entity
Cross-reference approach
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Set up a third relation as a “lookup table” for the
relationship
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Required for many-to-many relationships
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Binary 1:N Relationships
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Use the foreign key approach
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Identify which relation represents the entity on “many” side of the
relationship
Give that relation a foreign key pointing at the primary key on the
“one” side of the relationship
Or use cross-reference
EMPLOYEE
Ssn
Fname
M
Lname
Address
Dno
DEPARTMENT
Dname
Dnumber
MgrSsn
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Binary M:N Relationships
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Cross-reference approach
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For Entities E1 and E2 connected by Relationship R
Create a new relation for R
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Include as attributes foreign keys pointing at the primary keys of E1
and E2 – combination will be the primary key
Include any attributes tied to R
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Think of this as a “lookup table”
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EMPLOYEE
Ssn
Fname
M
Lname
Address
Dno
WORKS_ON
Ssn
Pnumber
Hours
PROJECT
Name
Pnumber
Location
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Multivalued Attributes
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Each multi-valued attribute A in the entity E1 gets its own
relation
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Relation includes the attribute A and a foreign key pointing at the
primary key of the relation associated with E1
Primary key of the new relation is a combination of A and the
foreign key
DEPARTMENT
Dname
Dnumber
MgrSsn
DEPT_LOCATIONS
Dno
Dlocation
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N-ary Relationships
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N-ary relationships modeled using crossreference approach
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Each n-ary relationship is made into a new relation
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Attributes of this relation include foreign keys pointing at the
primary keys of all the participating entity relations
Include all simple attributes as well
Primary key is usually a combination of all foreign keys
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Be careful – cardinality constraints may mean that we need to
leave some of these out
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Summary of ER-to-Relational
mapping
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