Review of Relational Algebra. Review of Relational Algebra. Review of Relational Algebra. Review of Relational Algebra. Review of Relational Algebra

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1 C 440: Database Management ystems eview of elational Algebra How to design a language to query a relational database? elational algebra Procedural, explain how results are obtained elational calculus Declarative, no need to specify the steps eview of elational Algebra Queries consist of a collection of operators Every operator accepts one or two relation instances as input and return a relation instance as output Combining these operators can form more complex queries eview of elational Algebra Basic operators ELECT (σ), POJECT (), ENAME () UNION ( U), INTEECTION ( I), MINU (-) CO PODUCT ( ) JOIN ( >< ), DIVIION ( ) EQUIJOIN, NATUAL JOIN (*) eview of elational Algebra Extended Generalized to include projection of functions Aggregate functions and grouping F ecursive closure operation OUTE JOIN LEFT OUTE JOIN ( >< ) IGHT OUTE JOIN ( >< ) FULL OUTE JOIN ( >< ) OUTE UNION eview of elational Algebra election σ GPA>3 tudents) Projection ID.5 (, Name, GPA( tudents)

2 eview of elational Algebra Display the ID, Name, and GPA of students with a GPA > 3.5 eview of elational Algebra Display the ID, Name, and GPA of students with a GPA > 3.5, Name, GPA( σ GPA 3. 5tudents) ID > eview of elational Algebra eview of elational Algebra eview of elational Algebra eview of elational Algebra

3 eview of elational Algebra eview of elational Algebra Mike Kathy TX O Mike Kathy TX O John TX Jean O eview of elational Algebra Mike TX Kathy O John TX Jean O eview of elational Algebra Union-compatibility ame number of fields ame domain for every corresponding field Mike TX Kathy O John TX Jean O eview of elational Algebra Intersection elational Algebra Intersection

4 elational Algebra Intersection needs to respect unioncompatibility, too. elational Algebra Difference elational Algebra elational Algebra Difference respects union-compatibility. Cross Product TX O TX TX TX O O O elational Algebra enaming: Change relation name only: New _ relation _ name Can be derived from cross-product and projection/selection More frequent than cross-product in practice Change attribute names only: ( New _ attribute name, New_ attribute _ 2 _ name,..., New_ attribute _ N _ name) Change both relation name and attribute names: New _ elation _ Name( New_ attribute name, New_ attribute _ 2 _ name,..., New_ attribute _ N _ name)

5 Conditional joins >< c = σ C ( ) ailors(sid:integer, sname:string,rating:integer,age:real) 2 Boats(bid:integer, bname: string, color: string) eserves(sid:integer, bid: integer, day: date) ><. sid =. sid Equijoins >< c = σ C ( ) ailors(sid:integer, sname:string,rating:integer,age:real) 2 Boats(bid:integer, bname: string, color: string) eserves(sid:integer, bid: integer, day: date) ><. sid =. sid Natural joins * ailors(sid:integer, sname:string,rating:integer,age:real) 2 Boats(bid:integer, bname: string, color: string) eserves(sid:integer, bid: integer, day: date) ailors(sid:integer, sname:string,rating:integer,age:real) 2 Boats(bid:integer, bname: string, color: string) eserves(sid:integer, bid: integer, day: date) boat 03 * ailors(sid:integer, sname:string,rating:integer,age:real) 2 Boats(bid:integer, bname: string, color: string) eserves(sid:integer, bid: integer, day: date) boat 03 (( σ 03 )* ) sname bid = ailors(sid:integer, sname:string,rating:integer,age:real) 2 Boats(bid:integer, bname: string, color: string) eserves(sid:integer, bid: integer, day: date) boat 03 (( σ 03( )) sname bid =

6 ailors(sid:integer, sname:string,rating:integer,age:real) 2 Boats(bid:integer, bname: string, color: string) eserves(sid:integer, bid: integer, day: date) a red or green boat ailors(sid:integer, sname:string,rating:integer,age:real) 2 Boats(bid:integer, bname: string, color: string) eserves(sid:integer, bid: integer, day: date) a red or green boat Tempboats (( σ color= ' red ' 2) ( σ color= ' sname (( Tempboats * )* ) green' )) 2 ailors(sid:integer, sname:string,rating:integer,age:real) 2 Boats(bid:integer, bname: string, color: string) eserves(sid:integer, bid: integer, day: date) a red or green boat ailors(sid:integer, sname:string,rating:integer,age:real) 2 Boats(bid:integer, bname: string, color: string) eserves(sid:integer, bid: integer, day: date) at least two boats Tempboats ( σ color= ' red ' color= ' sname (( Tempboats* )* ) green' ) 2 Division ailors(sid:integer, sname:string,rating:integer,age:real) 2 Boats(bid:integer, bname: string, color: string) eserves(sid:integer, bid: integer, day: date) at least two boats eservations sname ( sid, sname, bid ( sid= sid 2) ( bid bid 2) ( )) eservationpairs( sid, sname, bid, sid 2, sname2, bid 2) σ e servationpairs Find the sailors who have reserved all the boats sid bid bid sid 5 5 =

7 Division Find the sailors who have reserved all the boats sid bid bid 2 3 Tempsids ( sid, bid ) ( bid 2) ( Tempsids* ) sname = sid 5 Query Tree A graph consists of vertices and edges A graph is connected is there is a path between any pair of vertices that consists of edges in the graph A tree is a connected graph for which #V=#E+ Query Tree A query tree is a tree structure such that Leaf nodes represent the input relations Internal nodes represent the relational algebra operations. Extended elational Algebra Operators Generalized projection Allow functions T Teams(TID, Name, Conference, GamesWon, GamesLost) Teams TID, GamesWon+ GamesLost Extended elational Algebra Operators Aggregate functions and grouping Allow functions T Teams(TID, Name, Conference, GamesWon, GamesLost) C ( No _ Teams, Average_ Wins, Minimum_ Losses) ( ConferenceFCOUNT TID, AVGEAGEGamesWon, MINIMUM GamesLostTeams) Extended elational Algebra Operators Transitive closures : Find all the teams that were beat by OU Find all the teams that were beat by a team that was beat by OU Find all the teams that were beat by a team that was beat by a team that beat by OU. Can t do this in traditional relational algebra

8 Extended elational Algebra Operators OUTE JOIN List all the employees and the information about the department that they manage. If someone isn t managing a department, still show this. EMPLOYEE N EName John Tracy DEPT DID MsgN H DEV Extended elational Algebra Operators OUTE JOIN List all the employees and the information about the department that they manage. If someone isn t managing a department, still show this. EName, DID( EMPLOYEE >< N = MgrN DEPT) EMPLOYEE DEPT N EName DID MsgN John H Tracy DEV Extended elational Algebra Operators OUTE JOIN List all the employees and the information about the department that they manage. If someone isn t managing a department, still show this. EName, DID( EMPLOYEE >< N = MgrN DEPT) EULT EName Tracy DID DEV Extended elational Algebra Operators OUTE JOIN List all the employees and the information about the department that they manage. If someone isn t managing a department, still show this., ( EMPLOYEE EName DID >< N = MgrN DEPT) EULT EName John Tracy DID DEV Extended elational Algebra Operators Mapping E to Database chema OUTE UNION Mike Kathy TX O Mike TX Kathy O

9 Mapping E to Database schema Mapping E to Database chema Fundamental building blocks in E-diagrams: Entities trong weak Attributes imple Composite Multi-valued elationships Cardinality participation Mapping E to Database chema Mapping E to Database chema Fundamental building blocks in relational databases: Tables Attributes Primary keys econdary keys Foreign keys Non-key attributes Data types Map entities and relationships from E to tables in database schema Map attributes from E to attributes in database schema Mapping E to Database chema Mapping of egular Entities Mapping of entities egular Weak Mapping of relationships : :N M:N Mapping of multivalued attributes Mapping of N-ary elationship Types Create a table for each regular entity Use only simple attribute or the simple component of a composite attribute Determine a primary key If multiple keys, determine secondary keys Can be useful for indexing

10 Mapping of Weak Entities Create a table for each weak entity Use only simple attribute or the simple component of a composite attribute Include a foreign key attribute to owner entity Determine a primary key Partial key plus foreign key to owner entity If the owner is also a weak entity, then append its owner s primary key Mapping of M:N elationship Create a table Include foreign key to the participating entities These foreign keys form the primary key of the relationship

11 Mapping of :N elationship Method : Treat as M:N (is this a good way?) Method 2: Make a foreign key for the entity on the N-side to point to the primary key of the entity on the -side. Mapping of : elationship Method : Treat as M:N (is this a good way?) Method 2: Treat as :N (is this a good way?) Method 3: Make a foreign key in one entity to the primary key of another entity (is this a good way?) Put all attributes of the relationship to the table describing the entity with the foreign key

12 Mapping of Multivalued Attribute Create a table for each such attribute Make a foreign key to the entity which this attribute belongs Combine the foreign key and the attribute itself as the primary key of the table Mapping of N-ary Attribute Like binary relationship Create a table Make foreign key attributes to each of the participating entity Combine these foreign keys to form the primary key