🗊Презентация Relational Algebra

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Слайд 1





Lecture 6. Relational algebra
National Aviation University
Computer Science Faculty
Department of Software Engineering
Описание слайда:
Lecture 6. Relational algebra National Aviation University Computer Science Faculty Department of Software Engineering

Слайд 2





CONTENTS
Query languages in DB
Properties of binary operations
Relational algebra operations
Examples 
Equivalent transformation and optimization of relational algebra expressions
Описание слайда:
CONTENTS Query languages in DB Properties of binary operations Relational algebra operations Examples Equivalent transformation and optimization of relational algebra expressions

Слайд 3





Query languages
Language categories:
procedural (HOW to receive)
nonprocedural (WHAT to receive)
Formal languages:
relational algebra
relational calculus (tuple-oriented and domain-oriented)
Описание слайда:
Query languages Language categories: procedural (HOW to receive) nonprocedural (WHAT to receive) Formal languages: relational algebra relational calculus (tuple-oriented and domain-oriented)

Слайд 4





Relational algebra closure and properties of binary operations
Property of binary relations:

Operation  is commutative if А  В = B  A
Operation  is associative if (А  В)  С = А  (В  С)
Operation  is distributive with respect with other operation , if
А  (В  С ) = (А  В)  (А  С)
Описание слайда:
Relational algebra closure and properties of binary operations Property of binary relations: Operation  is commutative if А  В = B  A Operation  is associative if (А  В)  С = А  (В  С) Operation  is distributive with respect with other operation , if А  (В  С ) = (А  В)  (А  С)

Слайд 5





Relational algebra operations
Basic operations:
set-theoretic (union, intersection, difference)
projection
selection
cartesian product, 
join
division
Additional operations
assignment
renaming
generalized projection
outer join
…
Описание слайда:
Relational algebra operations Basic operations: set-theoretic (union, intersection, difference) projection selection cartesian product, join division Additional operations assignment renaming generalized projection outer join …

Слайд 6





Set-theoretic operations
Описание слайда:
Set-theoretic operations

Слайд 7





Union operation
Описание слайда:
Union operation

Слайд 8





Difference operation
Описание слайда:
Difference operation

Слайд 9





Intersection operation
Описание слайда:
Intersection operation

Слайд 10





Projection operation
Описание слайда:
Projection operation

Слайд 11





-comparability of attributes and tuples
Описание слайда:
-comparability of attributes and tuples

Слайд 12





Selection (restriction) operation
Описание слайда:
Selection (restriction) operation

Слайд 13





Cartesian product
Описание слайда:
Cartesian product

Слайд 14





Join operation
Описание слайда:
Join operation

Слайд 15





Join and natural join
Описание слайда:
Join and natural join

Слайд 16





Semijoin
Описание слайда:
Semijoin

Слайд 17





Image of the tuple
Описание слайда:
Image of the tuple

Слайд 18





Division operation (1)
Описание слайда:
Division operation (1)

Слайд 19





Division operation(2)
Описание слайда:
Division operation(2)

Слайд 20





Example of DB for RA queries
FAC (FNo, Name, Dean, Bld, Fund)
DEP (DNo, FNo, Name, Head, Bld, Fund)
TCH (TNo, DNo, Name, Post, Tel, Salary, Comm)
GRP (GNo, DNo, Course, Num, Quantity, CurNo)
SBJ (SNo, Name)
ROM (RNo, Num, Building, Seats)
LEC (TNo, GNo, SNo, RNo, Type, Day, Week)
Описание слайда:
Example of DB for RA queries FAC (FNo, Name, Dean, Bld, Fund) DEP (DNo, FNo, Name, Head, Bld, Fund) TCH (TNo, DNo, Name, Post, Tel, Salary, Comm) GRP (GNo, DNo, Course, Num, Quantity, CurNo) SBJ (SNo, Name) ROM (RNo, Num, Building, Seats) LEC (TNo, GNo, SNo, RNo, Type, Day, Week)

Слайд 21





Examples of queries  in RA (1)
Описание слайда:
Examples of queries in RA (1)

Слайд 22





Examples of queries  in RA (2)
Описание слайда:
Examples of queries in RA (2)

Слайд 23





Examples of queries  in RA (3)
Описание слайда:
Examples of queries in RA (3)

Слайд 24





Examples of division operation
Описание слайда:
Examples of division operation

Слайд 25





Additional operations 
Additional operations
Assignment
Renaming
Generalized projection
Outer join
…
Описание слайда:
Additional operations Additional operations Assignment Renaming Generalized projection Outer join …

Слайд 26





Assignment operation
Описание слайда:
Assignment operation

Слайд 27





Rename operation
Описание слайда:
Rename operation

Слайд 28





Generalized projection operation
Описание слайда:
Generalized projection operation

Слайд 29





Outer join
Описание слайда:
Outer join

Слайд 30





Outer join – example of ordinary join
Описание слайда:
Outer join – example of ordinary join

Слайд 31





Left outer join
Описание слайда:
Left outer join

Слайд 32


Relational Algebra, слайд №32
Описание слайда:

Слайд 33





Full outer join
Описание слайда:
Full outer join

Слайд 34





Equivalent transformations of 
relational expressions
1) Commutativity of selection: σF(σG(R))=σG(σF(R))=σF&G(R)

2) Commutativity of selection and projection:

	G(σF(R))=σF(G(R))=σF&G(R), если G  F

3) Distributivity of selection and product

	σF(R х S) = σF(R) x σF(S)

4) Distributivity of selection and set-theoretic operations:

	σF(R  S)=σF(R)  σF(S), σF(R  S)=σF(R)  σF(S)

5) Distributivity of selection and join:

	σF(R   S) = σF(R)   S, если условие F относится к R

6) Distributivity of projection and set-theoretic operations :

	F(R  S)=F(R)  F(S), F(R  S)=F(R)  F(S)
Описание слайда:
Equivalent transformations of relational expressions 1) Commutativity of selection: σF(σG(R))=σG(σF(R))=σF&G(R) 2) Commutativity of selection and projection: G(σF(R))=σF(G(R))=σF&G(R), если G  F 3) Distributivity of selection and product σF(R х S) = σF(R) x σF(S) 4) Distributivity of selection and set-theoretic operations: σF(R  S)=σF(R)  σF(S), σF(R  S)=σF(R)  σF(S) 5) Distributivity of selection and join: σF(R S) = σF(R) S, если условие F относится к R 6) Distributivity of projection and set-theoretic operations : F(R  S)=F(R)  F(S), F(R  S)=F(R)  F(S)

Слайд 35





Optimization of RA expressions
Описание слайда:
Optimization of RA expressions

Слайд 36





General rules of RA expressions optimization
General rules of RA expressions optimization:

Transform each selection σF1&...&Fn(E) to the sequence of 
selections σF1(... σFn(E)) 

Move each selection downwards of the tree as far as it is possible 
(thus (vertical) size of the relation is reduced). 

Adjacent selection and cartesian product are replaced by join.

Move each projection downwards of the tree as far as it 
is possible (thus (horizontal) size of the relation is reduced). 

Transform each cascade of adjacent selections and projections into 
single projection or selection with subsequent projection
Описание слайда:
General rules of RA expressions optimization General rules of RA expressions optimization: Transform each selection σF1&...&Fn(E) to the sequence of selections σF1(... σFn(E)) Move each selection downwards of the tree as far as it is possible (thus (vertical) size of the relation is reduced). Adjacent selection and cartesian product are replaced by join. Move each projection downwards of the tree as far as it is possible (thus (horizontal) size of the relation is reduced). Transform each cascade of adjacent selections and projections into single projection or selection with subsequent projection

Слайд 37





Relational Algebra: Summary
Relational Algebra:
 Formal language for handling data in relational model
 Procedural language, how to retrieve data
 No practical relevance for querying DB
 Formal basis for query optimization
Important terms & concepts:
 Union R  S, difference R – S, intersection R  S
 Projection <attribute list>(R)
 Selection σ<predicate>(R)
 Cartesian product R x S
 Joins R      <predicate> S
 Difference
Описание слайда:
Relational Algebra: Summary Relational Algebra: Formal language for handling data in relational model Procedural language, how to retrieve data No practical relevance for querying DB Formal basis for query optimization Important terms & concepts: Union R  S, difference R – S, intersection R  S Projection <attribute list>(R) Selection σ<predicate>(R) Cartesian product R x S Joins R <predicate> S Difference



Теги Relational Algebra
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