Chapter 4 Relational Algebra Chapter 4 in Textbook

Lilac Safadi Relational Algebra 2 Database Design Steps in building a database for an application: Real-world domain Conceptual model DBMS data model Create Schema (DDL) Modify data (DML)

Lilac Safadi Relational Algebra 3 Theoretical expressions where both operands are relations The output from one operation can become the input to another operation (nested relational algebra) Eight fundamental operations in relational algebra: Unary operations work on one relation Selection Projection Binary operations work on pairs of relations Cartesian productJoin UnionIntersection Set differenceDivision Relational Algebra

Lilac Safadi Relational Algebra 4 Algebra Operators abcabc xyxy aabbccaabbcc xyxyxyxyxyxy Cartesian Product a1 a2 a3 b1 b2 b3 b1 b2 b3 c1 c2 c3 a1 a2 a3 b1 b2 b3 c1 c2 c3 Join xyxy a aaabcaaabc xyzxyxyzxy Divide SelectionProject UnionIntersection Difference

Lilac Safadi Relational Algebra 5 Algebra Operators (Join) Cartesian Product AabAab B12B12 B113B113 CxyzCxyz TU AaaabbbAaaabbb B111222B B113113B Theta Join AaabAaab B112B112 CxyCxy Outer Join Natural Join AaAa B1B1 SemiJoin CxyzxyzCxyzxyz AbbAbb B22B22 B11B11 CxyCxy AaaAaa B11B11 B11B11 CxyCxy EquiJoin AaaAaa B11B11 CxyCxy

Lilac Safadi Relational Algebra 6 Selection Operation Return the tuples of R that satisfy a selection condition Denoted by  (R) Example: Select all staff with a salary greater than 10,000  salary > (STAFF)

Lilac Safadi Relational Algebra 7 SL21 SG37 SG14 SG5 StaffNo John Ann David Susan FName White Beech Ford Brand LNameSex M F M F DOB 1-Oct Nov May-58 3-Jun-40 Salary Selection Operation BrnNo D005 D003  salary > (STAFF)

Lilac Safadi Relational Algebra 8 Projection Operation Return the attributes of R Denoted by  (R) Example: Produce a list of salaries for all staff, showing only the staff number, first name, last name, and salary.  sno,fname,lname,salary (STAFF)

Lilac Safadi Relational Algebra 9 SL21 SG37 SG14 SNo John Ann David FName Salary Projection Operation LName White Ford Beech SA9 SG5 SL41 Mary Susan Julie Howe Lee Brand  sno,fname,lname,salary (STAFF)

Lilac Safadi Relational Algebra 10Question Produce a list of salaries for all staff greater than 10,000, showing only the staff number, first name, last name, and salary.

Lilac Safadi Relational Algebra 11 Union Operation Return a relation that includes all tuples that are either in R or in S, or in both R and S. Eliminate duplicate tuples. R & S must be union-compatible. Denoted by R  S R S R  S abcabc adfadf abcdfabcdf

Lilac Safadi Relational Algebra 12 Union Operation Example: List all cities where there is either a branch office or a property for rent.  city (BRANCH)   city (PROPERTY)

Lilac Safadi Relational Algebra 13 PA14 PL94 PG4 PG36 PG21 PropertyNo Holheld Argyll St Lawrence Monar Novar Street Aberdeen London Glasgow Bristol City PostCode AB7 5SU NW2 G11 9QX G32 4QX G12 Type House Flat House OwnerNo PROPERTY B001 B002 B003 BrnNo Deer Rd Argyll St Main St Street SW1 4EH CO46 CO87 CO40 CO93 CO87 PostCode AB2 3SU G11 9QX BRANCH Union Operation City London Glasgow Aberdeen City London Glasgow Aberdeen Bristol  city (BRANCH)   city (PROPERTY) BrnNo B001 B003

Lilac Safadi Relational Algebra 14Question List all addresses where there is a branch office or a property for rent in Glasgow city.

Lilac Safadi Relational Algebra 15 Difference Operation Return a relation that includes all tuples that are in R but NOT in S. R & S must be union-compatible. Denoted by R - S R S R - S abcabc adfadf bcbc

Lilac Safadi Relational Algebra 16 Difference Operation Example: List all cities where there is a property for rent but no branch office.  city (PROPERTY) -  city (BRANCH)

Lilac Safadi Relational Algebra 17 PA14 PL94 PG4 PG36 PG21 PropertyNo Holheld Argyll St Lawrence Monar Novar Street Aberdeen London Glasgow Bristol City PostCode AB7 5SU NW2 G11 9QX G32 4QX G12 Type House Flat House OwnerNo PROPERTY B001 B002 B003 BrnNo Deer Rd Argyll St Main St Street SW1 4EH CO46 CO87 CO40 CO93 CO87 PostCode AB2 3SU G11 9QX BRANCH Difference Operation City London Glasgow Aberdeen City Bristol  city (PROPERTY) -  city (BRANCH) BrnNo B001 B003

Lilac Safadi Relational Algebra 18 Intersection Operation Return a relation that includes all tuples that are in both R and S. R & S must be union-compatible. Denoted by R  S R S R  S abcabc adfadf a

Lilac Safadi Relational Algebra 19 Intersection Operation Example: List all cities where there is a branch office and at least one property for rent.  city (BRANCH)   city (PROPERTY)

Lilac Safadi Relational Algebra 20 PA14 PL94 PG4 PG36 PG21 PropertyNo Holheld Argyll St Lawrence Monar Novar Street Aberdeen London Glasgow Bristol City PostCode AB7 5SU NW2 G11 9QX G32 4QX G12 Type House Flat House OwnerNo PROPERTY B001 B002 B003 BrnNo Deer Rd Argyll St Main St Street SW1 4EH CO46 CO87 CO40 CO93 CO87 PostCode AB2 3SU G11 9QX BRANCH Intersection Operation City London Glasgow Aberdeen City  city (BRANCH)   city (PROPERTY) London Glasgow Aberdeen BrnNo B001 B003

Lilac Safadi Relational Algebra 21 Cartesian Product Operation Return a relation that is the concatenation of tuples from two relations R & S Denoted by R X S {a,b} X {1,2,3} = {(a,1), (a,2), (a,3), (b,1), (b,2), (b,3)}

Lilac Safadi Relational Algebra 22 Cartesian Product Operation Example: List the names and comments of all client who viewed a property. Step 1: Cartesian product  ClientNo, Fname, Lname (CLIENT) X  ClientNo, PrprtyNo, Comment (VIEW)  Client.ClientNo, Fname, Lname, View.ClientNo, PrprtyNo, Comment (CLIENT X VIEW) Step 2: Selection  Client.ClientNo=View.ClientNo (  ClientNo, Fname, Lname (CLIENT) X  ClientNo, PrprtyNo, Comment (VIEW) )

Lilac Safadi Relational Algebra 23 CR76 CO56 CR74 CR62 ClientNo John Aline Mike Mary FName Kay Stewart Ritchie Tregear LNameTelNo CLIENT CR56 CR76 CR56 ClientNo PA14 PG4 PrprtyNo Too small Comment Too remote No dining room VIEW Cartesian Product Operation ViewDate 24-May May Apr-01 CR62 CR56 PA14 PG3628-Apr May-01 Cardinality = 4 Tuples Degree = 3 Attributes (projected) Cardinality = 5 Tuples Degree = 3 Attributes (projected)

Lilac Safadi Relational Algebra 24 CR76 CR56 CR74 CR62 Client. ClientNo John Aline Mike Mary FName Kay Stewart Ritchie Tregear LName View. ClientNo PrprtyNo Comment CR56 CR76 CR56 PA14 PG4 Too small Too remote No dining room CR62 CR56 PA14 PG36 CR76JohnKay CR76JohnKay CR76JohnKay CR76JohnKay CR56 CR76 CR56 PA14 PG4 Too small Too remote No dining room CR62 CR56 PA14 PG36 CR56 CR76 CR56 PA14 PG4 Too small Too remote No dining room CR62 CR56 PA14 PG36 CR56 AlineStewart CR56 AlineStewart CR56 AlineStewart CR74 MikeRitchie CR74 MikeRitchie CR74 Mike Ritchie CR74Mike Ritchie CR74Mike Ritchie CR56 CR76 CR56 PA14 PG4 Too small Too remote No dining room CR62 CR56 PA14 PG36 CR62 Mary Tregear CR62 Mary Tregear CR62 Mary Tregear CR62 Mary Tregear  ClientNo, Fname, Lname (CLIENT) X  clientNo, PropertyNo, comment (VIEW)) Cardinality = 5 * 4 = 20 Tuple Degree = = 6 Attributes

Lilac Safadi Relational Algebra 25 Join Operation Return a relation that is the concatenation of tuples from two relations R & S that satisfy a certain condition Form of join operation: - Theta join - Equijoin - Natural join - Outer join - Semijoin

Lilac Safadi Relational Algebra 26 Theta join Operation Return a relation that includes all tuples that satisfy the logical condition F from the Cartesian product of R & S. Logical operators (  ) Denoted by R F S =  F (R X S)

Lilac Safadi Relational Algebra 27 Theta join Operation CLIENT(ClientNo, FName, Lname, TelNo) VIEW(ClientNo, PropertyNo, ViewDate, Comment) Example: List the names and comments of all renters who have viewed a property.  Client.ClientNo, Fname, Lname, View.ClientNo, PrprtyNo, Comment (CLIENT Client.ClientNo=View.ClientNo VIEW) Alternative:  Client.ClientNo=View.ClientNo (  ClientNo, Fname, Lname (CLIENT) X  ClientNo, PrprtyNo, Comment (VIEW))

Lilac Safadi Relational Algebra 28 Equijoin Operation A Theta join where the logical condition is equality (=). Example: List the names and comments of all renters who have viewed a property.  Client.ClientNo, Fname, Lname, View.ClientNo, PrprtyNo, Comment (CLIENT Client.ClientNo=View.ClientNo VIEW)

Lilac Safadi Relational Algebra 29 CR76 CR56 CR74 CR62 Client. ClientNo John Aline Mike Mary FName Kay Stewart Ritchie Tregear LName View. ClientNo PrprtyNo Comment CR56 CR76 CR56 PA14 PG4 Too small Too remote No dining room CR62 CR56 PA14 PG36 CR76JohnKay CR76JohnKay CR76JohnKay CR76JohnKay CR56 CR76 CR56 PA14 PG4 Too small Too remote No dining room CR62 CR56 PA14 PG36 CR56 CR76 CR56 PA14 PG4 Too small Too remote No dining room CR62 CR56 PA14 PG36 CR56 AlineStewart CR56 AlineStewart CR56 AlineStewart CR74 MikeRitchie CR74 MikeRitchie CR74 Mike Ritchie CR74Mike Ritchie CR74Mike Ritchie CR56 CR76 CR56 PA14 PG4 Too small Too remote No dining room CR62 CR56 PA14 PG36 CR62 Mary Tregear CR62 Mary Tregear CR62 Mary Tregear CR62 Mary Tregear  ClientNo, Fname, Lname (CLIENT) X  clientNo, PropertyNo, comment (VIEW))

Lilac Safadi Relational Algebra 30 CR76 CR56 Client. ClientNo John Aline FName Kay Stewart LName View. ClientNo PrprtyNo Comment CR76 CR56 PG4 PA14 Too remote Too small PG4 PA14CR62 No dining roomMary Tregear CR62  Client.ClientNo=View.ClientNo (  ClientNo, Fname, Lname (CLIENT) X  ClientNo, PrprtyNo, Comment (VIEW)) CR56 AlineStewart Equijoin Operation

Lilac Safadi Relational Algebra 31 Natural join Operation Equijoin of two relation R & S over all common attributes and values. One occurrence of each common attribute is eliminated from the result Denoted by R S Example: List the names and comments of all renters who have viewed a property.  ClientNo, Fname, Lname (CLIENT)  ClientNo, PrprtyNo, Comment (VIEW)

Lilac Safadi Relational Algebra 32 CR76 CR56 ClientNo John Aline FName Kay Stewart LName PrprtyNoComment PG4 PA14 Too remote Too small PG4 PA14 No dining room Mary Tregear CR62 CLIENT VIEW CR56 AlineStewart Natural join Operation TelNo ViewDate 20-Apr May01 24-May May-01

Lilac Safadi Relational Algebra 33 CR76 CR56 ClientNo John Aline FName Kay Stewart LName PrprtyNoComment PG4 PA14 Too remote Too small PG4 PA14 No dining roomMary Tregear CR62  ClientNo, Fname, Lname (CLIENT)  ClientNo, PrprtyNo, Comment (VIEW) CR56 AlineStewart Natural join Operation

Lilac Safadi Relational Algebra 34 Outer join Operation A natural join in which tuples from R that do not have matching values in the common attributes of S are included in the result relation. Missing values in S are set to null. Denoted by R S Example: Produce a status report on property viewings. (  PropertyNo, Street, City, CLientNo,ViewDate, Comment (PROPERTY) VIEW)

Lilac Safadi Relational Algebra 35 PA14 PL94 PG4 PG36 PG21 PropertyNo Holheld Argyll St Lawrence Monar Novar Street Aberdeen London Glasgow Bristol City PostCode AB7 5SU NW2 G11 9QX G32 4QX G12 Type House Flat House OwnerNo PROPERTY CO46 CO87 CO40 CO93 CO87 VIEW Outer Join Operation CR56 CR76 CR56 ClientNo PA14 PG4 PrprtyNo Too small Comment Too remote No dining room ViewDate 24-May May Apr-01 CR62PA14 14-May-01

Lilac Safadi Relational Algebra 36 PA14 PL94 PG4 PG36 PG21 PropertyNo Holheld Argyll St Lawrence Monar Novar Street Aberdeen London Glasgow Bristol City ClientNo CR56 null CR76 ViewDate 24-May-01 null 20-Apr-01 Comment Too small null Too remote Outer Join Operation PA14 HolheldAberdeenCR6214-May-01 No dining room null PG4 Lawrence Glasgow CR5626-May-01 null  PropertyNo, Street, City, CLientNo,ViewDate, Comment (PROPERTY) VIEW

Lilac Safadi Relational Algebra 37 Semijoin Operation Defines a relation that contains the tuples of R that participate in the join of R with S Denoted by R F S =  A (R F S) A is the set of attributes for R

Lilac Safadi Relational Algebra 38 Semijoin Operation Example: List the complete details of all properties who belong at the branch in Glasgow PROPERTY Property.BranchNo=Branch.BranchNo and Branch.city=‘Glasgow’ BRANCH Alternative: (  PropertyNo, Street, City,Postcode, Type, OwnerNo, BrnNo (PROPERTY Property.BranchNo=Branch.BranchNo and Branch.city=‘Glasgow’ BRANCH)

Lilac Safadi Relational Algebra 39 PA14 PL94 PG4 PG36 PG21 PropertyNo Holheld Argyll St Lawrence Monar Novar Street Aberdeen London Glasgow London City PostCode AB7 5SU NW2 G11 9QX G32 4QX G12 Type House Flat House OwnerNo PROPERTY B001 B002 B003 BrnNo Deer Rd Argyll St Main St Street SW1 4EH CO46 CO87 CO40 CO93 CO87 PostCode AB2 3SU G11 9QX BRANCH Semijoin Operation City London Glasgow Aberdeen BrnNo B002 B001 B003 B001

Lilac Safadi Relational Algebra 40 PG4 PG36 PropertyNo Lawrence Monar Street Glasgow City postcodel G11 9QX G32 4QX Type Flat OwnerNo CO40 CO93 Semijoin Operation BrnNo B003 PROPERTY Property.BranchNo=Branch.BranchNo and Branch.city=‘Glasgow’ BRANCH

Lilac Safadi Relational Algebra 41Question List details of branches managing properties of flat type

Lilac Safadi Relational Algebra 42 Division Operation Assume Relation R defined over attribute set A Relation S is defined over the attribute set B B  A C = A - B (attributes of R that are not of S) The division operation consists of the set of tuples from R defined over the attributes C that match the combination of every tuple in S Denoted by R S

Lilac Safadi Relational Algebra 43 Division Operation Example: Identify all clients who have veiwed all properties with three rooms (  ClientNo, PropertyNo (VIEW)) (  PropertyNo (  room=3 (PROPERTY)))

Lilac Safadi Relational Algebra 44 PA14 PL94 PG4 PG36 PG21 PropertyNo Holheld Argyll St Lawrence Monar Novar Street Aberdeen London Glasgow Bristol City postcode AB7 5SU NW2 G11 9QX G32 4QX G12 Type House Flat House OwnerNo PROPERTY CO46 CO87 CO40 CO93 CO87 VIEW Division Operation CR56 CR76 CR56 ClientNo PA14 PG4 PrprtyNo Too small Comment Too remote No dining room ViewDate 24-May May Apr-01 CR62PA14 14-May-01 Room CR56PG36 17-May-01

Lilac Safadi Relational Algebra 45 Division Operation VIEW CR56 CR76 CR56 ClientNo PA14 PG4 PrprtyNo CR62PA14 PROPERTY PG4 PG36 PrprtyNo CR56 ClientNo (  PropertyNo (  room=3 (PROPERTY))) (  ClientNo, PropertyNo (VIEW)) CR56PG36 (  ClientNo, PropertyNo (VIEW)) (  PropertyNo (  room=3 (PROPERTY)))

Lilac Safadi Relational Algebra 46Question Identify the clients that has been viewing all properties in Glasgow.

Lilac Safadi Relational Algebra 47 Summary of Relational Algebra Operations Operation Notation Selection Projection Union Difference Intersection Cartesian Product Theta join Equijoin Natural join Outer join Semijoin Division  (R)  (R) R  S R - S R  S R X S R F S R S