CS 4604: Introduction to Database Management Systemscourses.cs.vt.edu/~cs4604/Fall18/lectures/lecture-2.pdf · 2018-12-07 · • Conceptual model: In databases, structures are at

CS4604:IntroductiontoDatabaseManagementSystems

B.AdityaPrakashLecture#2:TheRelationalModeland

RelationalAlgebra

CourseOutline§  Weeks1–4:Query/

ManipulationLanguagesandDataModeling–  RelationalAlgebra–  Datadefinition–  ProgrammingwithSQL–  Entity-Relationship(E/R)approach

–  SpecifyingConstraints–  GoodE/Rdesign

§  Weeks5–8:Indexes,ProcessingandOptimization–  Storing–  Hashing/Sorting–  QueryOptimization–  NoSQLandHadoop

§  Week9-10:RelationalDesign–  FunctionalDependencies–  Normalizationtoavoidredundancy

§  Week11-12:ConcurrencyControl–  Transactions–  LoggingandRecovery

§  Week13–14:Students’choice–  PracticeProblems–  XML–  Dataminingandwarehousing

Prakash2018 VTCS4604 2

DataModel§  ADataModelisanotationfordescribingdataorinformation.

–  Structureofdata(e.g.arrays,structs)•  Conceptualmodel:Indatabases,structuresareatahigherlevel.

–  Operationsondata(ModificationsandQueries)•  LimitedOperations:Easeofprogrammersandefficiencyofdatabase.

–  Constraintsondata(whatthedatacanbe)§  Examplesofdatamodels

–  TheRelationalModel–  TheSemistructured-DataModel

•  XMLandrelatedstandards–  Object-RelationalModel


TheRelationalModel

§  Structure:Table(likeanarrayofstructs)§  Operations:Relationalalebgra(selection,projection,conditions,etc)

§  Constraints:E.g.,gradescanbeonly{A,B,C,F}

Prakash2018 VTCS4604

Student Course Grade

HermioneGrainger Potions A

DracoMalfoy Potions B

HarryPotter Potions A

RonWeasley Potions C

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TheSemi-structuredmodel

§  Structure:Treesorgraphs,tagsdefineroleplayedbydifferentpiecesofdata.

§  Operations:Followpathsintheimpliedtreefromoneelementtoanother.

§  Constraints:E.g.,canexpresslimitationsondatatypes


<CoursesTaken>

<Student>Hermione Grainger</Student>

<Course>Potions</Course>

<Grade>A</Grade>

<Student>Draco Malfoy</Student>

<Course>Potions</Course>

<Grade>B</Grade> ...

</CoursesTaken>

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Comparingthetwomodels

§  Flexibility:XMLcanrepresentgraphs§  Easeofuse:SQLenablesprogrammertoexpresswishesathighlevel.


TheRelationalModel§  Simple:Builtaroundasingleconceptformodelingdata:therelationortable.– Arelationaldatabaseisacollectionofrelations. – Eachrelationisatablewithrowsandcolumns.

§  Supportshigh-levelprogramminglanguage(SQL).– Limitedbutveryusefulsetofoperations

§  Hasanelegantmathematicaldesigntheory.§  MostcurrentDBMSarerelational(Oracle,IBMDB2,MSSQL)


Relations§  Arelationisatwo-dimensionaltable:

–  Relation==table.–  Attribute==columnname.–  Tuple==row(nottheheaderrow).

§  Database==collectionofrelations.§  Arelationhastwoparts:

–  Schemadefinescolumnheadsofthetable(attributes).–  Instancecontainsthedatarows(tuples,rows,orrecords)ofthetable.





RonWeasley Potions CPrakash2018 VTCS4604 8

SchemaCoursesTaken:§  Theschemaofarelationisthenameoftherelationfollowed

byaparenthesizedlistofattributes. CoursesTaken(Student, Course, Grade)

§  Adesigninarelationalmodelconsistsofasetofschemas.§  Suchasetofschemasiscalledarelationaldatabaseschema.







Relations:EquivalentRepresentationsCoursesTaken:

CoursesTaken(Student, Course, Grade)

§  Relationisasetoftuplesandnotalistoftuples.–  Orderinwhichwepresentthetuplesdoesnotmatter.–  Veryimportant!

§  Theattributesinaschemaarealsoaset(notalist).–  Schemaisthesameirrespectiveoforderofattributes. CoursesTaken(Student, Grade, Course)

–  Wespecifya“standard”orderwhenweintroduceaschema.§  Howmanyequivalentrepresentationsarethereforarelationwith

mattributesandntuples?






m! n! Prakash2018 VTCS4604 10

DegreeandCardinalityCoursesTaken:§  Degree/Arityisthenumberoffields/attributesinschema(=3

inthetableabove)§  Cardinalityisthenumberoftuplesinrelation(=4inthetable

above)







KeysofRelations§  Keysareoneformofintegrityconstraints(IC)

– Nopairoftuplesshouldhaveidenticalkeys§ WhatisthekeyforCoursesTaken?

– Studentifonlyonecourseintherelation– Pair(Student,Course)ifmultiplecourses– Whatifstudenttakessamecoursemanytimes?






RonWeasley Potions C12

KeysofRelations

§  Keyshelpassociatetuplesindifferentrelations


SID Student GPA

123 HermioneGrainger

3.9

111 DracoMalfoy 3.0

234 HarryPotter 3.7

456 RonWeasley 3.1

SID CID Grade

123 15-401 A

111 15-401 B

123 14-501 B

…. …. ….

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Example§  Create a database for managing class enrollments in a single

semester. You shouldkeep trackofall students (theirnames, Ids,and addresses) and professors (name, Id, department). Do notrecord the address of professors but keep track of their ages.Maintainrecordsofcoursesalso.Likewhatclassroomisassignedtoa course, what is the current enrollment, and which departmentoffersit.Atmostoneprofessorteacheseachcourse.Eachstudentevaluates the professor teaching the course. Note that all courseofferings in the semester are unique, i.e. course names andnumbers do not overlap. A course can have ≥ 0 pre-requisites,excludingitself.Astudentenrolledinacoursemusthaveenrolledin all its pre-requisites. Each student receives a grade in eachcourse.Thedepartmentsarealsounique,andcanhaveatmostonechairperson(ordept.head).Achairpersonisnot allowedtoheadtwoormoredepartments.


Example§  Create a database for managing class enrollments in a single

semester.Youshouldkeep trackofallstudents (theirnames, Ids,and addresses) and professors (name, Id, department). Do notrecord the address of professors but keep track of their ages.Maintain recordsofcourses also. Likewhat classroom is assignedtoacourse,whatisthecurrentenrollment,andwhichdepartmentoffersit.Atmostoneprofessorteacheseachcourse.Eachstudentevaluates the professor teaching the course.Note that all courseofferings in the semester are unique, i.e. course names andnumbers do not overlap. A course can have ≥ 0 pre-requisites,excludingitself.Astudentenrolledinacoursemusthaveenrolledin all its pre-requisites. Each student receives a grade in eachcourse. The departments are also unique, and can have at mostonechairperson (ordept.head).A chairperson isnot allowed toheadtwoormoredepartments.


RelationalDesignfortheExample§  Students(PID:string,Name:string,Address:string)

§  Professors(PID:string,Name:string,Office:string,Age:integer,DepartmentName:string)

§  Courses(Number:integer,DeptName:string,CourseName:string,Classroom:string,Enrollment:integer)

§  Teach(ProfessorPID:string,Number:integer,DeptName:string)

§  Take(StudentPID:string,Number: integer,DeptName:string,Grade:string,ProfessorEvaluation:integer)

§  Departments(Name:string,ChairmanPID:string)

§  PreReq(Number:integer,DeptName:string,PreReqNumber:integer, PreReqDeptName:string)


RelationalDesignExample:Keys?§  Students(PID:string,Name:string,Address:string)








RelationalDesign:Keys?§  Students(PID:string,Name:string,Address:string)








IssuestoConsiderintheDesign§  CanwemergeCoursesandTeachsinceeachprofessorteachesatmostonecourse?

§  Doweneedaseparaterelationtostoreevaluations?§  Howcanwehandlepre-requisitesthatare“or”s,e.g.,youcantakeCS4604ifyouhavetakeneitherCS3114orCS2606?

§  Howdowegeneralizethisschematohandledataovermorethanonesemester?

§  Whatmodificationsdoestheschemaneedifmorethanoneprofessorcanteachacourse?



Formalquerylanguages

§  Howdowecollectinformation?§  Eg.,findssn’sofpeoplein415§  (recall:everythingisaset!)§  Onesolution:Rel.algebra,ie.,setoperators§  Q1:Whichones??§  Q2:whatisaminimalsetofoperators?

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§  .§  .§  .§  setunionU§  setdifference‘-’

Relationaloperators

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Example:

FT-STUDENTSsn Name

129 peters main str239 lee 5th ave

PT-STUDENTSsn Name Address

123 smith main str234 jones forbes ave

§  Q:findallstudents(partorfulltime)§  A:PT-STUDENTunionFT-STUDENT

22


Observations:

§  twotablesare‘unioncompatible’iftheyhavethesameattributes(‘domains’)

§  Q:howaboutintersectionU

23


Observations:

§  A:redundant:§  STUDENTintersectionSTAFF=

STUDENT STAFF

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Observations:

§  A:redundant:§  STUDENTintersectionSTAFF=

STUDENT STAFF

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Observations:

§  A:redundant:§  STUDENTintersectionSTAFF=STUDENT-(STUDENT-STAFF)

STUDENT STAFF

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Observations:

§  A:redundant:§  STUDENTintersectionSTAFF=STUDENT-(STUDENT-STAFF)

Doublenegation:We’llseeitagain,later…

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§  .§  .§  .§  setunion§  setdifference‘-’

Relationaloperators

U

28


Otheroperators?

§  eg,findallstudentson‘Mainstreet’§  A:‘selection’

)('' STUDENTstrmainaddress=σ

STUDENTSsn Name Address


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Otheroperators?

§  Notice:selection(andrestofoperators)expecttables,andproducetables(->canbecascaded!!)

§  Forselection,ingeneral:

)(RELATIONconditionσ

30


Selection-examples

§  Findall‘Smiths’on‘MainSt.’

σ name='Smith '∧ address='Main st. ' (STUDENT )

‘condition’canbeanybooleancombinationof‘=‘,‘>’,‘>=‘,‘<>’,...

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§  selection§  .§  .§  setunion§  setdifferenceR-S

Relationaloperators

)(Rconditionσ

RUS

32


§  selectionpicksrows-howaboutcolumns?§  A:‘projection’-eg.:findsallthe‘ssn’-removingduplicates

Relationaloperators

)(STUDENTssnπ



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Cascading:‘findssnofstudentson‘mainst.’

Relationaloperators

π ssn (σ address='main st ' (STUDENT ))



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§  selection§  projection§  .§  setunion§  setdifferenceR-S

Relationaloperators

)(Rconditionσ

)(Rlistatt−π

RUS

35


Arewedoneyet?Q:Giveaquerywecannotansweryet!

Relationaloperators

36


A:anyqueryacrosstwoormoretables,eg.,‘findnamesofstudentsin4604’

Q:whatextraoperatordoweneed??

Relationaloperators



SSN c-id grade123 4604 A234 5614 B

37


A:anyqueryacrosstwoormoretables,eg.,‘findnamesofstudentsin4604’

Q:whatextraoperatordoweneed??A:surprisingly,cartesianproductisenough!

Relationaloperators



SSN c-id grade123 4604 A234 5614 B

38


Cartesianproduct

§  eg.,dog-breeding:MALExFEMALE§  givesallpossiblecouples

MALEnamespikespot

FEMALEnamelassieshiba

x =M.name F.namespike lassiespike shibaspot lassiespot shiba

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sowhat?

§  Eg.,howdowefindnamesofstudentstaking4604?

40


Cartesianproduct

§  A:

Ssn Name Address ssn cid grade123 smith main str 123 4604 A234 jones forbes ave 123 4604 A123 smith main str 234 5614 B234 jones forbes ave 234 5614 B

)(......... .. TAKESxSTUDENTssnTAKESssnSTUDENT =σ

41


Cartesianproduct

..σ cid=4604(σ STUDENT .ssn=TAKES.ssn (STUDENT x TAKES))


42


π name(σ cid=4604(σ STUDENT .ssn=TAKES.ssn (STUDENT x TAKES)))


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§  selection§  projection§  cartesianproductMALExFEMALE§  setunion§  setdifferenceR-S

FUNDAMENTALRelationaloperators

)(Rconditionσ)(Rlistatt−π

RUS

44


Relationalops

§  Surprisingly,theyareenough,tohelpusansweralmostanyquerywewant!!

§  derived/convenienceoperators:– setintersection–  join(thetajoin,equi-join,naturaljoin)– ‘rename’operator– division

)(' RRρSR ÷

45


Joins

§  Equijoin:SR bSaR .. =▹◃ )(.. SRbSaR ×= =σ

46


Cartesianproduct

§  A: )(......... .. TAKESxSTUDENTssnTAKESssnSTUDENT =σ


47


Joins

§  Equijoin:§  theta-joins:generalizationofequi-join-anycondition

SR bSaR .. =▹◃ )(.. SRbSaR ×= =σSR θ▹◃

θ

48


Joins

§  verypopular:naturaljoin:RS§  likeequi-join,butitdropsduplicatecolumns:STUDENT(ssn,name,address)TAKES(ssn,cid,grade)

49


Joins

§  nat.joinhas5attributes TAKESSTUDENT ▹◃

TAKESSTUDENT ssnTAKESssnSTUDENT .. =▹◃equi-join:6


50


NaturalJoins-nit-picking

§  ifnoattributesincommonbetweenR,S:nat.join->cartesianproduct

51


Overview-rel.algebra

§  fundamentaloperators§  derivedoperators

–  joinsetc–  rename– division

§  examples

52


Renameop.

§  Q:why?§  A:shorthand;self-joins;…§  forexample,findthegrand-parentsof‘Tom’,givenPC(parent-id,child-id)

)(BEFOREAFTERρ

53


Renameop.

§  PC(parent-id,child-id) PCPC▹◃

PCp-id c-idMary TomPeter MaryJohn Tom

PCp-id c-idMary TomPeter MaryJohn Tom

54


Renameop.

§  first,WRONGattempt:§  (why?howmanycolumns?)§  SecondWRONGattempt:

PCPC▹◃

PCPC idpPCidcPC −=− ..▹◃

55


Renameop.

§  weclearlyneedtwodifferentnamesforthesametable-hence,the‘rename’op.

PCPC idpPCidcPCPC −=− ..11 )( ▹◃ρ

56





§  examples

57


Division

§  Rarelyused,butpowerful.§  Example:findsuspicioussuppliers,ie.,suppliersthatsuppliedallthepartsinA_BOMB

58


Division

SHIPMENTs# p#s1 p1s2 p1s1 p2s3 p1s5 p3

ABOMBp#p1p2

BAD_Ss#s1÷ =

59

Example:findsuspicioussuppliers,ie.,suppliersthatsuppliedallthepartsinA_BOMB


Division

§  Observations:~reverseofcartesianproduct§  Itcanbederivedfromthe5fundamentaloperators(!!)

§  How?

60


Division

§  Answer:

§  Observation:find‘good’suppliers,andsubtract!(doublenegation)

]))([()( )()()( rsrrsr SRSRSR −×−=÷ −−− πππ

61


Division

§  Answer:

§  Observation:find‘good’suppliers,andsubtract!(doublenegation)



ABOMBp#p1p2

BAD_Ss#s1÷ =

62


Division

§  Answer:



ABOMBp#p1p2

BAD_Ss#s1÷ =

Allsuppliers

Allbadparts

63

Table‘r’Table‘s’


Division

§  Answer:



ABOMBp#p1p2

BAD_Ss#s1÷ =

allpossiblesuspiciousshipments

64



Division

§  Answer:



ABOMBp#p1p2

BAD_Ss#s1÷ =

allpossiblesuspiciousshipmentsthatdidn’thappen

65



Division

§  Answer:



ABOMBp#p1p2

BAD_Ss#s1÷ =

allsupplierswhomissedatleastonesuspiciousshipment,

i.e.:‘good’suppliers

66






§  examples

67


Sampleschema



CLASSc-id c-name units

4513 s.e. 24512 o.s. 2

SSN c-id grade123 4513 A234 4513 B

findnamesofstudentsthattake4604

68

TAKES


Examples

§  findnamesofstudentsthattake4604

69


Examples

§  findnamesofstudentsthattake4604

π name[σ c−id=4604 (STUDENT ▹◃TAKES)]

70


Sampleschema




4613 s.e. 24612 o.s. 2

SSN c-id grade123 4613 A234 4613 B

findcoursenamesof‘smith’

71

TAKES


Examples

§  findcoursenamesof‘smith’

π c−name[σ name='smith ' (

STUDENT ▹◃TAKES ▹◃CLASS)]

72


Examples

§  findssnof‘overworked’students,ie.,thattake4612,4613,4604

73


Examples

§  findssnof‘overworked’students,ie.,thattake4612,4613,4604:almostcorrectanswer:

σ c−name=4612 (TAKES)∩σ c−name=4613(TAKES)∩σ c−name=4604 (TAKES)

74


Examples

§  findssnof‘overworked’students,ie.,thattake4612,4613,4604-Correctanswer:

π ssn[σ c−name=4612 (TAKES)]∩π ssn[σ c−name=4613(TAKES)]∩π ssn[σ c−name=4604 (TAKES)]

75


Examples

§  findssnofstudentsthatworkatleastashardasssn=123,ie.,theytakeallthecoursesofssn=123,andmaybemore

76


Sampleschema




4613 s.e. 24612 o.s. 2

SSN c-id grade123 4613 A234 4613 B

77

TAKES


Examples

§  findssnofstudentsthatworkatleastashardasssn=123(ie.,theytakeallthecoursesofssn=123,andmaybemore

)]([)]([ 123, TAKESTAKES ssnidcidcssn =−− ÷ σππ

78


Conclusions

§  Relationalmodel:onlytables(‘relations’)§  relationalalgebra:powerful,minimal:5operatorscanhandlealmostanyquery!

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CS 4604: Introduction to Database Management Systemscourses.cs.vt.edu/~cs4604/Fall18/lectures/lecture-2.pdf · 2018-12-07 · • Conceptual model: In databases, structures are at

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