n-ary relations and their applications
DESCRIPTION
n-ary Relations and Their Applications. Rosen 8.2. n-ary relations. We can have relation between more than just 2 sets. A binary relation involves 2 sets and can be described by a set of pairs A ternary relation involves 3 sets and can be described by a set of triples … - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: n-ary Relations and Their Applications](https://reader035.vdocument.in/reader035/viewer/2022062310/5681682d550346895dddc7e3/html5/thumbnails/1.jpg)
n-ary Relations and Their Applications
Rosen 8.2
![Page 2: n-ary Relations and Their Applications](https://reader035.vdocument.in/reader035/viewer/2022062310/5681682d550346895dddc7e3/html5/thumbnails/2.jpg)
n-ary relations
We can have relation between more than just 2 sets
A binary relation involves 2 sets and can be described by a set of pairsA ternary relation involves 3 sets and can be described by a set of triples…
An n-ary relation involves n sets and can be described by a set of n-tuples
Relations are used to represent computer databases
Also used to represent constraints!
![Page 3: n-ary Relations and Their Applications](https://reader035.vdocument.in/reader035/viewer/2022062310/5681682d550346895dddc7e3/html5/thumbnails/3.jpg)
n-ary relations n-ary Relations
ndomainsAAA
AAAaryn
AAA
n
n
n
isrelation theof degree Therelation theof theare ,,, sets The
product cartesian theofsubset a isrelation An
sets be ,,Let
21
21
2,1
![Page 4: n-ary Relations and Their Applications](https://reader035.vdocument.in/reader035/viewer/2022062310/5681682d550346895dddc7e3/html5/thumbnails/4.jpg)
n-ary relations n-ary Relations
cbacbaNNNR
such that ),,( triplesof consisting on relation thebe Let
Note: N is the set of natural numbers {0,1,2,3,…}
An example
}),3,2,1(,),4,2,0(),3,2,0(,),3,1,0(),2,1,0{( R
R)3,4,2(
Note: R could be considered as an extensional representation of the ternary relation a<b<c, assuming domains are finite and really quite small
The relation has degree 3
The domains of the relation are the set of natural numbers
![Page 5: n-ary Relations and Their Applications](https://reader035.vdocument.in/reader035/viewer/2022062310/5681682d550346895dddc7e3/html5/thumbnails/5.jpg)
n-ary relations n-ary Relations
)0()(such that ),,,(tuples-4 of consisting on relation thebe Let
dcbadcbadcbaZNZNR
Note: N is the set of natural numbers {0,1,2,3,…} Z is the set of integers {…,-2,-1,0,1,2,…}
An example
Note: R could be considered as an extensional representation of the ternary relation a<b<c, assuming domains are finite and really quite small
The relation has degree 4RRR
)9,3,6,6()3,3,11,5(
)0,1,1,0(
![Page 6: n-ary Relations and Their Applications](https://reader035.vdocument.in/reader035/viewer/2022062310/5681682d550346895dddc7e3/html5/thumbnails/6.jpg)
Relational databases
Database is made up of records.Typical operations on a database are
• find records that satisfy a given criteria• delete records• add records• update records
Some everyday databases• student records• health records• tax information• telephone directories• banking records• …
Databases may be represented using the relational model
![Page 7: n-ary Relations and Their Applications](https://reader035.vdocument.in/reader035/viewer/2022062310/5681682d550346895dddc7e3/html5/thumbnails/7.jpg)
![Page 8: n-ary Relations and Their Applications](https://reader035.vdocument.in/reader035/viewer/2022062310/5681682d550346895dddc7e3/html5/thumbnails/8.jpg)
![Page 9: n-ary Relations and Their Applications](https://reader035.vdocument.in/reader035/viewer/2022062310/5681682d550346895dddc7e3/html5/thumbnails/9.jpg)
Relational databases The relational data model
Database made up of records, they are n-tuples, made up of fields
Student record might look as follows
(name,metricNo,faculty,gpa)
(Jones,200401986,Arts,4.9)(Lee,200408972,Science,3.6)(Kuhns,200501728,Humanities,5.0)(Moore,200308327,Science,5.5)
relations (in relDB) also called tables
gpa is an attribute
![Page 10: n-ary Relations and Their Applications](https://reader035.vdocument.in/reader035/viewer/2022062310/5681682d550346895dddc7e3/html5/thumbnails/10.jpg)
Relational databases The relational data model
2.99Psychology786576Stevens3.90sMathematic678543Rao3.49sMathematic453876Goodfriend3.49ScienceComputer 102147Chou3.45Physics888323Adams3.88ScienceComputer 231455AckermannGPADeptmetricNoName
Example from the book
Attributes: name, metric No, Dept and GPA
![Page 11: n-ary Relations and Their Applications](https://reader035.vdocument.in/reader035/viewer/2022062310/5681682d550346895dddc7e3/html5/thumbnails/11.jpg)
Relational databases The relational data model
2.99Psychology786576Stevens3.90sMathematic678543Rao3.49sMathematic453876Goodfriend3.49ScienceComputer 102147Chou3.45Physics888323Adams3.88ScienceComputer 231455AckermannGPADeptmetricNoName
primary key:An attribute/domain/column is a primary key whenthe value of this attribute uniquely defines tuplesi.e. no two tuples have the same value for that attribute
Name cannot be a primary key, neither can Dept or GPSmetricNo is a primary key
![Page 12: n-ary Relations and Their Applications](https://reader035.vdocument.in/reader035/viewer/2022062310/5681682d550346895dddc7e3/html5/thumbnails/12.jpg)
Relational databases The relational data model
2.99Psychology786576Stevens3.90sMathematic678543Rao3.49sMathematic453876Goodfriend3.49ScienceComputer 102147Chou3.45Physics888323Adams3.88ScienceComputer 231455AckermannGPADeptmetricNoName
The current collection of n-tuples (records) in the relation (table)is called the extension of the relation
The permanent aspects of the relation (table) such as the attribute namesis called the intention of the relation
![Page 13: n-ary Relations and Their Applications](https://reader035.vdocument.in/reader035/viewer/2022062310/5681682d550346895dddc7e3/html5/thumbnails/13.jpg)
Relational databases The relational data model
2.99Psychology786576Stevens3.90sMathematic678543Rao3.49sMathematic453876Goodfriend3.49ScienceComputer 102147Chou3.45Physics888323Adams3.88ScienceComputer 231455AckermannGPADeptmetricNoName
A composite key is a combination of attributesThat uniquely define tuples
![Page 14: n-ary Relations and Their Applications](https://reader035.vdocument.in/reader035/viewer/2022062310/5681682d550346895dddc7e3/html5/thumbnails/14.jpg)
Relational databases Operations on n-ary relations
2.99Psychology786576Stevens3.90sMathematic678543Rao3.49sMathematic453876Goodfriend3.49ScienceComputer 102147Chou3.45Physics888323Adams3.88ScienceComputer 231455AckermannGPADeptmetricNoName
CRtuplesnarynRS
RCarynR
c
condition esatisfy th that from all ofrelation new the to maps operator selection The
satisfy.must in elementsthat condition a andrelation an be Let
Selection
![Page 15: n-ary Relations and Their Applications](https://reader035.vdocument.in/reader035/viewer/2022062310/5681682d550346895dddc7e3/html5/thumbnails/15.jpg)
Relational databases Operations on n-ary relations
2.99Psychology786576Stevens3.90sMathematic678543Rao3.49sMathematic453876Goodfriend3.49ScienceComputer 102147Chou3.45Physics888323Adams3.88ScienceComputer 231455AckermannGPADeptmetricNoName
CRtuplesnarynRS
RCarynR
c
condition esatisfy th that from all ofrelation new the to maps operator selection The
satisfy.must in elementsthat condition a andrelation an be Let
Selection
3.45GPA condition theis where operator selection Apply theCSc
3.90sMathematic678543Rao3.49sMathematic453876Goodfriend3.49ScienceComputer 102147Chou
3.88ScienceComputer 231455AckermannGPADeptmetricNoName
![Page 16: n-ary Relations and Their Applications](https://reader035.vdocument.in/reader035/viewer/2022062310/5681682d550346895dddc7e3/html5/thumbnails/16.jpg)
Relational databases Operations on n-ary relations
2.99Psychology786576Stevens3.90sMathematic678543Rao3.49sMathematic453876Goodfriend3.49ScienceComputer 102147Chou3.45Physics888323Adams3.88ScienceComputer 231455AckermannGPADeptmetricNoName
Projection
nmaaatuplemaaatuplen
iiiPprojection
m
m
iii
n
miii
where),,,( the to),,,( themaps
where The
21
21
21
21
It strips out specific columns
![Page 17: n-ary Relations and Their Applications](https://reader035.vdocument.in/reader035/viewer/2022062310/5681682d550346895dddc7e3/html5/thumbnails/17.jpg)
Relational databases Operations on n-ary relations
2.99Psychology786576Stevens3.90sMathematic678543Rao3.49sMathematic453876Goodfriend3.49ScienceComputer 102147Chou3.45Physics888323Adams3.88ScienceComputer 231455AckermannGPADeptmetricNoName
Projection
nmaaatuplemaaatuplen
iiiPprojection
m
m
iii
n
miii
where),,,( the to),,,( themaps
where The
21
21
21
21
4,1 projection Apply the P
2.99Stevens3.90Rao3.49Goodfriend3.49Chou3.45Adams3.88AckermannGPAName
![Page 18: n-ary Relations and Their Applications](https://reader035.vdocument.in/reader035/viewer/2022062310/5681682d550346895dddc7e3/html5/thumbnails/18.jpg)
Relational databases Operations on n-ary relationsJoin
Joins two tables/relations together, matching up on specific attributes
575sMathematic518ScienceComputer 551Physics544Physics617Psychology501Psychology412Zoology335Zoology
RosenRosenGrammerGrammerFaberFaberCruzCruz
CourseDeptLecturer
08.00A100412Zoology09.00A100335Zoology11.00A110617Psychology15.00A100501Psychology16.00B505544Physics16.00N521611sMathematic15.00N502575sMathematic14.00N521518ScienceComputer TimeRoomCourseDept
4)Defn p.534Rosen (seematch attributes goverlappin the where from come attributes last theand come attributes first thesuch that
degree ofrelation new a delivers and andly respective
relations and are and where),(operator join The
pSpnRpm
pnmnpmp
arynarymSRSRJ p
![Page 19: n-ary Relations and Their Applications](https://reader035.vdocument.in/reader035/viewer/2022062310/5681682d550346895dddc7e3/html5/thumbnails/19.jpg)
Relational databases Operations on n-ary relationsJoin
R
RosenRosenGrammerGrammerFaberFaberCruzCruz
CourseDeptLecturer
Relation
575sMathematic518ScienceComputer 551Physics544Physics617Psychology501Psychology412Zoology335Zoology
S
TimeRoomCourseDept
Relation
08.00A100412Zoology09.00A100335Zoology11.00A110617Psychology15.00A100501Psychology16.00B505544Physics16.00N521611sMathematic15.00N502575sMathematic14.00N521518ScienceComputer
),(2 SRJ
15.00N502575sMathematicRosen14.00N521518ScienceComputer Rosen16.00B505544PhysicsGrammer11.00A110617PsychologyFaber15.00A100501PsychologyFaber08.00A100412ZoologyCruz09.00A100335ZoologyCruzTimeRoomCourseDeptLecturer
![Page 20: n-ary Relations and Their Applications](https://reader035.vdocument.in/reader035/viewer/2022062310/5681682d550346895dddc7e3/html5/thumbnails/20.jpg)
Explain the previous slide
Explain how what we do differs from what will be presented in IM2