Entity-Relationship Model

Modeling

• A database can be modeled as:
• a collection of entities,
• relationship among entities.
• An entity is an object that exists and is distinguishable from other objects.
• Example: specific person, company, event, plant
• Entities have attributes
• Example: people have names and addresses
• An entity set is a set of entities of the same type that share the same properties.
• Example: set of all persons, companies, trees, holidays

Entity Sets instructor and student

instructor_ID instructor_name student-ID student_name

Relationship Sets

• A relationship is an association among several entities

Example:� 44553 (Peltier) advisor 22222 (Einstein) � student entity relationship set instructor entity

• A relationship set is a mathematical relation among n ≥ 2 entities, each taken from entity sets

{(e₁, e₂, … e_n) | e₁ ∈ E₁, e₂ ∈ E₂, …, e_n ∈ E_n}��where (e₁, e₂, …, e_n) is a relationship

• Example:

(44553,22222) ∈ advisor

Relationship Set advisor

Relationship Sets

• An attribute can also be property of a relationship set.
• For instance, the advisor relationship set between entity sets instructor and student may have the attribute date which tracks when the student started being associated with the advisor

Degree of a Relationship Set

• binary relationship
• involve two entity sets (or degree two).
• most relationship sets in a database system are binary.
• Relationships between more than two entity sets are rare. Most relationships are binary.
• Example: students work on research projects under the guidance of an instructor.
• relationship proj_guide is a ternary relationship between instructor, student, and project

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Attributes

• An entity is represented by a set of attributes, that is descriptive properties possessed by all members of an entity set.
• Example:

instructor = (ID, name, street, city, salary )� course= (course_id, title, credits)

• Domain – the set of permitted values for each attribute
• Attribute types:
• Simple and composite attributes.
• Single-valued and multivalued attributes
• Example: multivalued attribute: phone_numbers
• Derived attributes
• Can be computed from other attributes
• Example: age, given date_of_birth

Composite Attributes

Mapping Cardinality Constraints

• Express the number of entities to which another entity can be associated via a relationship set.
• Most useful in describing binary relationship sets.
• For a binary relationship set the mapping cardinality must be one of the following types:
• One to one
• One to many
• Many to one
• Many to many

Mapping Cardinalities

One to one

One to many

Note: Some elements in A and B may not be mapped to any

elements in the other set

Mapping Cardinalities

Many to one

Many to many

Note: Some elements in A and B may not be mapped to any

elements in the other set

Keys

• A super key of an entity set is a set of one or more attributes whose values uniquely determine each entity.
• A candidate key of an entity set is a minimal super key
• ID is candidate key of instructor
• course_id is candidate key of course
• Although several candidate keys may exist, one of the candidate keys is selected to be the primary key.

Keys for Relationship Sets

• The combination of primary keys of the participating entity sets forms a super key of a relationship set.
• (s_id, i_id) is the super key of advisor
• NOTE: this means a pair of entity sets can have at most one relationship in a particular relationship set.
• Example: if we wish to track multiple meeting dates between a student and her advisor, we cannot assume a relationship for each meeting. We can use a multivalued attribute though
• Must consider the mapping cardinality of the relationship set when deciding what are the candidate keys
• Need to consider semantics of relationship set in selecting the primary key in case of more than one candidate key

Redundant Attributes

• Suppose we have entity sets
• instructor, with attributes including dept_name
• department

and a relationship

• inst_dept relating instructor and department
• Attribute dept_name in entity instructor is redundant since there is an explicit relationship inst_dept which relates instructors to departments
• The attribute replicates information present in the relationship, and should be removed from instructor
• BUT: when converting back to tables, in some cases the attribute gets reintroduced, as we will see.

E-R Diagrams

• Rectangles represent entity sets.
• Diamonds represent relationship sets.
• Attributes listed inside entity rectangle
• Underline indicates primary key attributes

Entity With Composite, Multivalued, and Derived Attributes

Relationship Sets with Attributes

Cardinality Constraints

• We express cardinality constraints by drawing either a directed line (→), signifying “one,” or an undirected line (—), signifying “many,” between the relationship set and the entity set.
• One-to-one relationship:
• A student is associated with at most one instructor via the relationship advisor
• A student is associated with at most one department via stud_dept

One-to-One Relationship

• one-to-one relationship between an instructor and a student
• an instructor is associated with at most one student via advisor
• and a student is associated with at most one instructor via advisor

One-to-Many Relationship

• one-to-many relationship between an instructor and a student
• an instructor is associated with several (including 0) students via advisor
• a student is associated with at most one instructor via advisor,

Many-to-One Relationships

• In a many-to-one relationship between an instructor and a student,
• an instructor is associated with at most one student via advisor,
• and a student is associated with several (including 0) instructors via advisor

Many-to-Many Relationship

• An instructor is associated with several (possibly 0) students via advisor
• A student is associated with several (possibly 0) instructors via advisor

Participation of an Entity Set in a Relationship Set

• Total participation (indicated by double line): every entity in the entity set participates in at least one relationship in the relationship set
• E.g., participation of section in sec_course is total
• every section must have an associated course
• Partial participation: some entities may not participate in any relationship in the relationship set
• Example: participation of instructor in advisor is partial

E-R Diagram with a Ternary Relationship

Weak Entity Sets

• An entity set that does not have a primary key is referred to as a weak entity set.
• The existence of a weak entity set depends on the existence of a identifying entity set
• It must relate to the identifying entity set via a total, one-to-many relationship set from the identifying to the weak entity set
• Identifying relationship depicted using a double diamond
• The discriminator (or partial key) of a weak entity set is the set of attributes that distinguishes among all the entities of a weak entity set.
• The primary key of a weak entity set is formed by the primary key of the strong entity set on which the weak entity set is existence dependent, plus the weak entity set’s discriminator.

Weak Entity Sets

• We underline the discriminator of a weak entity set with a dashed line.
• We put the identifying relationship of a weak entity in a double diamond.
• Primary key for section – (course_id, sec_id, semester, year)

Weak Entity Sets

• Note: the primary key of the strong entity set is not explicitly stored with the weak entity set, since it is implicit in the identifying relationship.
• If course_id were explicitly stored, section could be made a strong entity, but then the relationship between section and course would be duplicated by an implicit relationship defined by the attribute course_id common to course and section

E-R Diagram for a University Enterprise

Reduction to Relational Schemas

Reduction to Relation Schemas

• Entity sets and relationship sets can be expressed uniformly as relation schemas that represent the contents of the database.
• A database which conforms to an E-R diagram can be represented by a collection of schemas.
• For each entity set and relationship set there is a unique schema that 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.

Representing Entity Sets With Simple Attributes

• A strong entity set reduces to a schema with the same attributes�student(ID, name, tot_cred)
• A weak entity set becomes a table that includes a column for the primary key of the identifying strong entity set �section ( course_id, sec_id, sem, year )

Representing Relationship Sets

• 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.
• Example: schema for relationship set advisor

advisor = (s_id, i_id)

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 inst_dept, add an attribute dept_name to the schema arising from entity set instructor

Redundancy of Schemas

• For one-to-one relationship sets, either side can be chosen to act as the “many” side
• That is, 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
• The schema corresponding to a relationship set linking a weak entity set to its identifying strong entity set is redundant.
• Example: The section schema already contains the attributes that would appear in the sec_course schema

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Composite and Multivalued Attributes

• Composite attributes are flattened out by creating a separate attribute for each component attribute
• Example: given entity set instructor with 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
• Prefix omitted if there is no ambiguity
• Ignoring multivalued attributes, extended instructor schema is
• instructor(ID, � first_name, middle_initial, last_name,� street_number, street_name, � apt_number, city, state, zip_code, � date_of_birth)

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Composite and 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 multivalued attribute M
• Example: Multivalued attribute phone_number of instructor is represented by a schema:� inst_phone= ( ID, phone_number)
• Each value of the multivalued attribute maps to a separate tuple of the relation on schema EM
• For example, an instructor entity with primary key 22222 and phone numbers 456-7890 and 123-4567 maps to two tuples: � (22222, 456-7890) and (22222, 123-4567)

Multivalued Attributes

• Special case:entity time_slot has only one attribute other than the primary-key attribute, and that attribute is multivalued
• Optimization: Don’t create the relation corresponding to the entity, just create the one corresponding to the multivalued attribute
• time_slot(time_slot_id, day, start_time, end_time)
• Caveat: time_slot attribute of section (from sec_time_slot) cannot be a foreign key due to this optimization

Design Issues

• Use of entity sets vs. attributes�����

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• Use of phone as an entity allows extra information about phone numbers (plus multiple phone numbers)

Design Issues

• Use of entity sets vs. relationship sets�Possible guideline is to designate a relationship set to describe an action that occurs between entities

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Design Issues

• Binary versus n-ary relationship sets�Although it is possible to replace any nonbinary (n-ary, for n > 2) relationship set by a number of distinct binary relationship sets, a n-ary relationship set shows more clearly that several entities participate in a single relationship.
• Placement of relationship attributes

e.g., attribute date as attribute of advisor or as attribute of student

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