Gitte ChristensenDyalog Ltd

Managing external data Part 1

Design of Databases

Purpose• To give you a crash course in data analysis

and databases• After part 1 Design of Databases you will

be able to analyse and organise data based on a requirement spec or use case.

• After part 2 Database programming you will be able to use relational data in your APL applications

• After part 3 Database Implementation you will be able to choose between different storage methods based on structure and use of data and performance considerations

Agenda

• The Relational Model– Entity/Relation model– Convert E/R to table structure– Relational Algebra

• Semistructured data• Multidimensional data

Data Models

• A Database models some portion of the real world.

• Data Model is link between user’s view of the world and bits stored in computer.

• We will concentrate on the Relational Model

Data Models• A data model is a collection of concepts

for describing data.• A database schema is a description of a

particular collection of data, using a given data model.

• The relational model of data is the most widely used model today.– Main concept: relation, basically a

table with rows and columns.– Every relation has a schema, which

describes the columns, or fields.

Levels of Abstraction• Views describe how

users see the data.

• Conceptual schema defines logical structure

• Physical schema describes the files and indexes used.

• (sometimes called the ANSI/SPARC model)

Physical Schema

Conceptual Schema

View 1 View 2 View 3

DB

Users

Data Independence• A Simple Idea:

Applications should be insulated from how data is structured and stored.

• Logical data independence: Protection from changes in logical structure of data.

• Physical data independence: Protection from changes in physical structure of data.

Physical Schema

Conceptual Schema

View 1 View 2 View 3

DB

Entity-Relationship Model

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Purpose of E/R Model

• The E/R model allows us to sketch database designs.– Kinds of data and how they connect.– Not how data changes.

• Designs are pictures called entity-relationship diagrams.

• Later: convert E/R designs to relational DB designs.

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Entity Sets

• Entity = “thing” or object.• Entity set = collection of similar entities.

– Similar to a class in object-oriented languages.

• Attribute = property of (the entities of) an entity set.– Attributes are simple values, e.g. integers or

character strings.

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E/R Diagrams

• In an entity-relationship diagram:

– Entity set = rectangle.

– Attribute = oval, with a line to the rectangle representing its entity set.

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Example

• Entity set Beers has two attributes, name and manf (manufacturer).

• Each Beers entity has values for these two attributes, e.g. (Bud, Anheuser-Busch)

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Beers

name manf

Relationships• A relationship connects two or more

entity sets.• It is represented by a diamond, with

lines to each of the entity sets involved.

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Example

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Drinkers addrname

Beers

manfname

Bars

name

license

addr

Note:license =beer, full,none

Sells Bars sell somebeers.

Likes

Drinkers likesome beers.Frequents

Drinkers frequentsome bars.

Relationship Set• The current “value” of an entity set is

the set of entities that belong to it.– Example: the set of all bars in our

database.

• The “value” of a relationship is a set of lists of currently related entities, one from each of the related entity sets.

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Example• For the relationship Sells, we might

have a relationship set like:

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Bar BeerJoe’s Bar BudJoe’s Bar MillerSue’s Bar BudSue’s Bar Pete’s AleSue’s Bar Bud Lite

Case Movie Database• We want to create a movie database

which will allow our users to find information about movies

• Each movie has a title, a production year, lenght in minutes, whether it is color or b/w and an owner, a studio

• We have adresses for the studios and the actors

EntityName

AttriAbuteAttributeName

Relationship Draw a model of the Movies database using these symbols

Multiway Relationships• Sometimes, we need a relationship

that connects more than two entity sets.

• Suppose that drinkers will only drink certain beers at certain bars.– Our three binary relationships Likes,

Sells, and Frequents do not allow us to make this distinction.

– But a 3-way relationship would.19

Example

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Bars Beers

Drinkers

name nameaddr manf

name addr

license

Preferences

A Typical Relationship Set

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Bar Drinker BeerJoe’s Bar Ann MillerSue’s Bar Ann BudSue’s Bar Ann Pete’s AleJoe’s Bar Bob BudJoe’s Bar Bob MillerJoe’s Bar Cal MillerSue’s Bar Cal Bud Lite

Case Movie Database• In each movie there are actors who

are contracted by the studios• Add this relationship to your model

Many-Many Relationships• Focus: binary relationships, such as

Sells between Bars and Beers.• In a many-many relationship, an

entity of either set can be connected to many entities of the other set.– E.g., a bar sells many beers; a beer is

sold by many bars.

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In Pictures:

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many-many

Many-One Relationships• Some binary relationships are many -

one from one entity set to another.• Each entity of the first set is

connected to at most one entity of the second set.

• But an entity of the second set can be connected to zero, one, or many entities of the first set.

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In Pictures:

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many-one

Example

• Favorite, from Drinkers to Beers is many-one.

• A drinker has at most one favorite beer.

• But a beer can be the favorite of any number of drinkers, including zero.

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One-One Relationships

• In a one-one relationship, each entity of either entity set is related to at most one entity of the other set.

• Example: Relationship Best-seller between entity sets Manfs (manufacturer) and Beers.– A beer cannot be made by more than one

manufacturer, and no manufacturer can have more than one best-seller (assume no ties).

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In Pictures:

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one-one

Representing “Multiplicity”• Show a many-one relationship by an

arrow entering the “one” side.• Show a one-one relationship by

arrows entering both entity sets.• Rounded arrow = “exactly one,” i.e.,

each entity of the first set is related to exactly one entity of the target set.

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Example

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Drinkers BeersLikes

Favorite

Example• Consider Best-seller between Manfs

and Beers.• Some beers are not the best-seller of

any manufacturer, so a rounded arrow to Manfs would be inappropriate.

• But a beer manufacturer has to have a best-seller.

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In the E/R Diagram

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Manfs BeersBest-seller

Case Movie Database• Add arrows to your diagram so it

reflects the kind of relations between the entities

Attributes on Relationships• Sometimes it is useful to attach an

attribute to a relationship.• Think of this attribute as a property

of tuples in the relationship set.

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Example

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Bars BeersSells

price

Price is a function of both the bar and the beer,not of one alone.

Equivalent Diagrams Without Attributes on Relationships• Create an entity set representing

values of the attribute.• Make that entity set participate in

the relationship.

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Example

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Bars BeersSells

price

PricesNote convention: arrowfrom multiway relationship= “all other entity setstogether determine aunique one of these.”

Roles• Sometimes an entity set appears

more than once in a relationship.• Label the edges between the

relationship and the entity set with names called roles.

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Example

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Drinkers

Married

husband wife

Relationship Set

Husband WifeBob AnnJoe Sue… …

Example

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Drinkers

Buddies

1 2

Relationship Set

Buddy1 Buddy2Bob AnnJoe SueAnn BobJoe Moe… …

Case Movie Database• The actors can be contracted either

by the studio producing the movie or by another studio who rents the actor to the producing studio

• We would like to record what the actor is paid for appearing in a movie

• Update your model to reflect the new facts

Subclasses• Subclass = special case = fewer

entities = more properties.• Example: Ales are a kind of beer.

– Not every beer is an ale, but some are.– Let us suppose that in addition to all the

properties (attributes and relationships) of beers, ales also have the attribute color.

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Subclasses in E/R Diagrams• Assume subclasses form a tree.

– I.e., no multiple inheritance.

• Isa triangles indicate the subclass relationship.– Point to the superclass.

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Example

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Beers

Ales

isa

name manf

color

Case Movie Database• For some movies like cartoons we

have a different kind of actor, voices.• Design a subclass to reflect this fact

ISA

E/R Vs. Object-Oriented Subclasses• In OO, objects are in one class only.

– Subclasses inherit from superclasses.

• In contrast, E/R entities have representatives in all subclasses to which they belong.– Rule: if entity e is represented in a

subclass, then e is represented in the superclass.

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Example

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Beers

Ales

isa

name manf

color

Pete’s Ale

Keys• A key is a set of attributes for one

entity set such that no two entities in this set agree on all the attributes of the key.– It is allowed for two entities to agree on

some, but not all, of the key attributes.

• We must designate a key for every entity set.

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Keys in E/R Diagrams

• Underline the key attribute(s).• In an Isa hierarchy, only the root

entity set has a key, and it must serve as the key for all entities in the hierarchy.

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Example: name is Key for Beers

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Beers

Ales

isa

name manf

color

Example: a Multi-attribute Key

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Courses

dept number hours room

• Note that hours and room could also serve as a key, but we must select only one key.

Case Movie Database• Add keys to your diagram

Weak Entity Sets• Occasionally, entities of an entity set

need “help” to identify them uniquely.• Entity set E is said to be weak if in

order to identify entities of E uniquely, we need to follow one or more many-one relationships from E and include the key of the related entities from the connected entity sets.

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Example

• name is almost a key for football players, but there might be two with the same name.

• number is certainly not a key, since players on two teams could have the same number.

• But number, together with the team name related to the player by Plays-on should be unique.

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In E/R Diagrams

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Players TeamsPlays-on

name namenumber

• Double diamond for supporting many-one relationship.• Double rectangle for the weak entity set.

Weak Entity-Set Rules• A weak entity set has one or more many-

one relationships to other (supporting) entity sets.– Not every many-one relationship from a weak

entity set need be supporting.

• The key for a weak entity set is its own underlined attributes and the keys for the supporting entity sets.– E.g., (player) number and (team) name is a key

for Players in the previous example.

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Case Movie Database• We would like to record which

camera crews shot a particular movie• Camera crews are numbered within

each studio• Add these facts to your diagram

Design Techniques1. Avoid redundancy.2. Limit the use of weak entity sets.3. Don’t use an entity set when an

attribute will do.

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Avoiding Redundancy

• Redundancy occurs when we say the same thing in two or more different ways.

• Redundancy wastes space and (more importantly) encourages inconsistency.– The two instances of the same fact may

become inconsistent if we change one and forget to change the other.

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Example: Good

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Beers ManfsManfBy

name

This design gives the address of each manufacturer exactly once.

name addr

Example: Bad

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Beers ManfsManfBy

name

This design states the manufacturer of a beer twice: as an attribute and as a related entity.

name

manf

addr

Example: Bad

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Beers

name

This design repeats the manufacturer’s address once for each beer and loses the address if there are temporarily no beers for a manufacturer.

manf manfAddr

Entity Sets Versus Attributes• An entity set should satisfy at least

one of the following conditions:– It is more than the name of something;

it has at least one nonkey attribute.or

– It is the “many” in a many-one or many-many relationship.

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Example: Good

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Beers ManfsManfBy

name

•Manfs deserves to be an entity set because of the nonkey attribute addr.•Beers deserves to be an entity set because it is the “many” of the many-one relationship ManfBy.

name addr

Example: Good

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Beers

name

There is no need to make the manufacturer an entity set, because we record nothing about manufacturers besides their name.

manf

Example: Bad

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Beers ManfsManfBy

name

Since the manufacturer is nothing but a name, and is not at the “many” end of any relationship, it should not be an entity set.

name

Don’t Overuse Weak Entity Sets• Beginning database designers often doubt

that anything could be a key by itself.– They make all entity sets weak, supported by

all other entity sets to which they are linked.

• In reality, we usually create unique ID’s for entity sets.– Examples include social-security numbers,

automobile VIN’s etc.

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When Do We Need Weak Entity Sets?

• The usual reason is that there is no global authority capable of creating unique ID’s.

• Example: it is unlikely that there could be an agreement to assign unique player numbers across all football teams in the world.

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Break

How to translate ER Model to Relational Model

Concepts

Relational Model is made up of tables

• A row of table = a relational instance/tuple

• A column of table = an attribute• A table = a schema/relation• Cardinality = number of rows• Degree = number of columns

Example

SID Name Major GPA

1234 John CS 2.8

5678 Mary EE 3.6

tuple/relational instance

Attribute

4 Degree

Cardinality =

2

A Schema / Relation

From ER Model to Relational ModelSo… how do we convert an ER diagram into

a table?? Simple!!Basic Ideas:• Build a table for each entity set• Build a table for each relationship set if necessary

(more on this later)• Make a column in the table for each attribute in

the entity set• Indivisibility Rule and Ordering Rule• Primary Key

Example – Strong Entity Set

SID Name Major GPA

1234 John CS 2.8

5678 Mary EE 3.6

Student

SID Name

Major GPA

Advisor Professor

SSN Name

Dept

SSN Name Dept

9999 Smith Math

8888 Lee CS

Representation of Weak Entity Set• Weak Entity Set Cannot exists alone• To build a table/schema for weak entity

set – Construct a table with one column for each

attribute in the weak entity set– Remember to include discriminator– Augment one extra column on the right side of

the table, put in there the primary key of the Strong Entity Set (the entity set that the weak entity set is depending on)

– Primary Key of the weak entity set = Discriminator + foreign key

Example – Weak Entity Set

Age Name Parent_SID

10 Bart 1234

8 Lisa 5678

Student

SID Name

Major GPA

NameAge

Childrenowns

Primary key of Children is Parent_SID + Name

Representation of Relationship Set

--This is a little more complicated--• Unary/Binary Relationship set

– Depends on the cardinality and participation of the relationship

– Two possible approaches

• N-ary (multiple) Relationship set– Primary Key Issue

• Identifying Relationship– No relational model representation necessary

Representing Relationship SetUnary/Binary Relationship• For one-to-one relationship w/out total participation

– Build a table with two columns, one column for each participating entity set’s primary key. Add successive columns, one for each descriptive attributes of the relationship set (if any).

• For one-to-one relationship with one entity set having total participation– Augment one extra column on the right side of the

table of the entity set with total participation, put in there the primary key of the entity set without complete participation as per to the relationship.

Example – One-to-One Relationship Set

SID Maj_ID Co S_Degree

9999 07 1234

8888 05 5678

Student

SID Name

Major GPA

ID Code

Majorstudy

Primary key can be either SID or Maj_ID_Co

Degree

Example – One-to-One Relationship Set

SID Name Major GPA LP_S/N Hav_Cond

9999 Bart Economy -4.0 123-456 Own

8888 Lisa Physics 4.0 567-890 Loan

Student

SID Name

Major GPA

S/N #

LaptopHave

* Primary key can be either SID or LP_S/N

Condition

Brand

1:1 Relationship

Representing Relationship SetUnary/Binary Relationship• For one-to-many relationship w/out total

participation – Same thing as one-to-one

• For one-to-many/many-to-one relationship with one entity set having total participation on “many” side– Augment one extra column on the right

side of the table of the entity set on the “many” side, put in there the primary key of the entity set on the “one” side as per to the relationship.

Example – Many-to-One Relationship Set

SID Name Major GPA Pro_SSN Ad_Sem

9999 Bart Economy -4.0 123-456 Fall 2006

8888 Lisa Physics 4.0 567-890 Fall 2005

Student

SID Name

Major GPA

SSN

Professor

* Primary key of this table is SID

Semester

Name

N:1 Relationship

Dept

Advisor

Representing Relationship SetUnary/Binary Relationship• For many-to-many relationship

– Same thing as one-to-one relationship without total participation.

– Primary key of this new schema is the union of the foreign keys of both entity sets.

– No augmentation approach possible…

Representing Relationship SetN-ary Relationship• Intuitively Simple

– Build a new table with as many columns as there are attributes for the union of the primary keys of all participating entity sets.

– Augment additional columns for descriptive attributes of the relationship set (if necessary)

– The primary key of this table is the union of all primary keys of entity sets that are on “many” side

– That is it, we are done.

Example – N-ary Relationship Set

P-Key1 P-Key2 P-Key3 A-Key D-Attribute

9999 8888 7777 6666 Yes

1234 5678 9012 3456 No

E-Set 1

P-Key1

Another Set

* Primary key of this table is P-Key1 + P-Key2 + P-Key3

D-Attribute

A relationship

A-Key

E-Set 2

P-Key2

E-Set 3

P-Key3

Representing Relationship SetIdentifying Relationship• This is what you have to know

– You DON’T have to build a table/schema for the identifying relationship set once you have built a table/schema for the corresponding weak entity set

– Reason:• A special case of one-to-many with total participation• Reduce Redundancy

Representing Composite Attribute• Relational Model Indivisibility Rule Applies• One column for each component attribute• NO column for the composite attribute itself

Professor

SSN Name

Address

SSN Name Street City

9999 Dr. Smith 50 1st St. Fake City

8888 Dr. Lee 1 B St. San Jose

Street City

Representing Multivalue Attribute• For each multivalue attribute in an entity

set/relationship set– Build a new relation schema with two columns– One column for the primary keys of the entity

set/relationship set that has the multivalue attribute

– Another column for the multivalue attributes. Each cell of this column holds only one value. So each value is represented as an unique tuple

– Primary key for this schema is the union of all attributes

Example – Multivalue attribute

SID Name Major GPA

1234 John CS 2.8

5678 Homer EE 3.6

Student

SID Name

Major GPA

Stud_SID Children

1234 Johnson

1234 Mary

5678 Bart

5678 Lisa

5678 Maggie

Children

The primary key for this table is Student_SID + Children, the union of all attributes

Representing Class Hierarchy• Two general approaches depending on

disjointness and completeness– For non-disjoint and/or non-complete class hierarchy:

• create a table for each super class entity set according to normal entity set translation method.

• Create a table for each subclass entity set with a column for each of the attributes of that entity set plus one for each attributes of the primary key of the super class entity set

• This primary key from super class entity set is also used as the primary key for this new table

Example

SSN SID Status Major GPA

1234 9999 Full CS 2.8

5678 8888 Part EE 3.6

Student

SID Status

Major GPA

SSN Name Gender

1234 Homer Male

5678 Marge Female

Person

Gender

SSN Name

ISA

Case Movie Database• Convert your E/R diagram to

relational tables

Relational Algebra

Relational Algebra

Relational Algebra is :•the formal description of how a relational database operates•the mathematics which underpin SQL operations.

Operators in relational algebra are not necessarily the same as SQL operators, even if they have the same name.

Terminology

• Relation - a set of tuples.• Tuple - a collection of attributes which

describe some real world entity.• Attribute - a real world role played by a

named domain.• Domain - a set of atomic values.• Set - a mathematical definition for a

collection of objects which contains no duplicates.

Operators - Write

• INSERT - provides a list of attribute values for a new tuple in a relation. This operator is the same as SQL.

• DELETE - provides a condition on the attributes of a relation to determine which tuple(s) to remove from the relation. This operator is the same as SQL.

• MODIFY - changes the values of one or more attributes in one or more tuples of a relation, as identified by a condition operating on the attributes of the relation. This is equivalent to SQL UPDATE.

Operators - Retrieval

There are two groups of operations:• Mathematical set theory based relations:

UNION, INTERSECTION, DIFFERENCE, and CARTESIAN PRODUCT.

• Special database operations: SELECT (not the same as SQL SELECT), PROJECT, and JOIN.

Relational SELECT

SELECT is used to obtain a subset of the tuples of a relation that satisfy a select condition.For example, find all employees born after 1st Jan 1950:

SELECT dob > ’01/JAN/1950’ (employee)

Relational PROJECTThe PROJECT operation is used to select a subset of the attributes of a relation by specifying the names of the required attributes.For example, to get a list of all employees surnames and employee numbers:

PROJECT surname,empno (employee)

SELECT and PROJECT

FROM employeeWHERE depno = 1;

SELECT empno

PROJECT empno (SELECT depno = 1 (employee))

Mapping this back to SQL gives:

SELECT and PROJECT can be combined together. For example, to get a list of employee numbers for employees in department number 1:

Set Operations - semanticsConsider two relations R and S.• UNION of R and S

the union of two relations is a relation that includes all the tuples that are either in R or in S or in both R and S. Duplicate tuples are eliminated.

• INTERSECTION of R and Sthe intersection of R and S is a relation that includes all tuples that are both in R and S.

• DIFFERENCE of R and Sthe difference of R and S is the relation that contains all the tuples that are in R but that are not in S.

SET Operations - requirementsFor set operations to function correctly the relations R and S must be union compatible. Two relations are union compatible if

– they have the same number of attributes– the domain of each attribute in column

order is the same in both R and S.

UNION Example

INTERSECTION Example

DIFFERENCE Example

CARTESIAN PRODUCT

The Cartesian Product is also an operator which works on two sets. It is sometimes called the CROSS PRODUCT or CROSS JOIN.

It combines the tuples of one relation with all the tuples of the other relation.

CARTESIAN PRODUCT Example

JOIN OperatorJOIN is used to combine related tuples from two

relations:• In its simplest form the JOIN operator is just the cross

product of the two relations.• As the join becomes more complex, tuples are

removed within the cross product to make the result of the join more meaningful.

• JOIN allows you to evaluate a join condition between the attributes of the relations on which the join is undertaken.

The notation used is R JOIN join condition S

JOIN Example

Natural Join

Invariably the JOIN involves an equality test, and thus is often described as an equi-join. Such joins result in two attributes in the resulting relation having exactly the same value. A ‘natural join’ will remove the duplicate attribute(s).– In most systems a natural join will require that the

attributes have the same name to identify the attribute(s) to be used in the join. This may require a renaming mechanism.

– If you do use natural joins make sure that the relations do not have two attributes with the same name by accident.

OUTER JOINsNotice that much of the data is lost when applying a join to two relations. In some cases this lost data might hold useful information. An outer join retains the information that would have been lost from the tables, replacing missing data with nulls.

There are three forms of the outer join, depending on which data is to be kept.•LEFT OUTER JOIN - keep data from the left-hand table•RIGHT OUTER JOIN - keep data from the right-hand table•FULL OUTER JOIN - keep data from both tables

OUTER JOIN Example 1

OUTER JOIN Example 2

Semistructured data

Root

cf mh sw

Carrie Fisher

address address

name

city

street

MapleHollywood

LocustMalibu

city

star

starmovie

title year

Star Wars1977

Mark HamillOak

Brentwood

name

street city

street

starIn

starOf

starIn

starOf

Multidimensional data

End of Part 1