Relational Model

Relational Model

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  RELATIONAL MODEL-CONT Additional toChapter 2 ICT 2073 Prepare by : Ms. Siti Hajar Binti Ismail
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  RELATIONAL QUERY LANGUAGES Query languages: Allow manipulation and retrieval of data from a database.  Relational model supports simple, powerful QLs:  Strong formal foundation based on logic.  Allows for much optimization.  Query Languages != programming languages!  QLs not expected to be “Turing complete”.  QLs not intended to be used for complex calculations.  QLs support easy, efficient access to large data sets.
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  FORMAL RELATIONAL QUERYLANGUAGES  Two mathematical Query Languages form the basis for “real” languages (e.g. SQL), and for implementation:  Relational Algebra: More operational (procedural), very useful for representing execution plans.  Relational Calculus: Lets users describe what they want, rather than how to compute it: Non-operational, declarative.
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  PRELIMINARIES  A queryis applied to relation instances, and the result of a query is also a relation instance.  Schemas of input relations for a query are fixed.  The schema for the result of a given query is also fixed! - determined by definition of query language constructs.  Positional vs. named-field notation:  Positional notation easier for formal definitions, named-field notation more readable.  Both used in SQL
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  EXAMPLE INSTANCES  “Sailors”and “Reserves” relations for our examples.  We’ll use positional or named field notation, assume that names of fields in query results are `inherited’ from names of fields in query input relations. sid sname rating age 22 dustin 7 45.0 31 lubber 8 55.5 58 rusty 10 35.0 sid sname rating age 28 yuppy 9 35.0 31 lubber 8 55.5 44 guppy 5 35.0 58 rusty 10 35.0 sid bid day 22 101 10/10/96 58 103 11/12/96 R1 S1 S2
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  RELATIONAL ALGEBRA  Basicoperations:  Selection ( ) Selects a subset of rows from relation.  Projection ( ) Deletes unwanted columns from relation.  Cross-product ( ) Allows us to combine two relations.  Set-difference ( ) Tuples in reln. 1, but not in reln. 2.  Union ( ) Tuples in reln. 1 and in reln. 2.  Additional operations:  Intersection, join, division, renaming: Not essential, but (very!) useful.  Since each operation returns a relation, operations can be composed: algebra is “closed”.     
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  PROJECTION  Deletes attributesthat are not in projection list.  Schema of result contains exactly the fields in the projection list, with the same names that they had in the input relation.  Projection operator has to eliminate duplicates! real systems typically don’t do duplicate elimination unless the user explicitly asks for it (by DISTINCT). sname rating yuppy 9 lubber 8 guppy 5 rusty 10 sname rating S , ( )2 age 35.0 55.5 age S( )2
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  SELECTION  Selects rowsthat satisfy selection condition.  No duplicates in result! Why?  Schema of result identical to schema of input relation.  What is Operator composition?  Selection is distributive over binary operators  Selection is commutative rating S 8 2( ) sid sname rating age 28 yuppy 9 35.0 58 rusty 10 35.0 sname rating yuppy 9 rusty 10  sname rating rating S , ( ( )) 8 2
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  UNION, INTERSECTION, SET-DIFFERENCE All of these operations take two input relations, which must be union-compatible:  Same number of fields.  `Corresponding’ fields have the same type.  What is the schema of result? sid sname rating age 22 dustin 7 45.0 31 lubber 8 55.5 58 rusty 10 35.0 44 guppy 5 35.0 28 yuppy 9 35.0 sid sname rating age 31 lubber 8 55.5 58 rusty 10 35.0 S S1 2 S S1 2 sid sname rating age 22 dustin 7 45.0 S S1 2
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  CROSS-PRODUCT (CARTESIAN PRODUCT) Each row of S1 is paired with each row of R1.  Result schema has one field per field of S1 and R1, with field names `inherited’ if possible.  Conflict: Both S1 and R1 have a field called sid.  ( ( , ), )C sid sid S R1 1 5 2 1 1   (sid) sname rating age (sid) bid day 22 dustin 7 45.0 22 101 10/10/96 22 dustin 7 45.0 58 103 11/12/96 31 lubber 8 55.5 22 101 10/10/96 31 lubber 8 55.5 58 103 11/12/96 58 rusty 10 35.0 22 101 10/10/96 58 rusty 10 35.0 58 103 11/12/96  Renaming operator:
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  JOINS: USED TOCOMBINE RELATIONS  Condition Join:  Result schema same as that of cross-product.  Fewer tuples than cross-product, might be able to compute more efficiently  Sometimes called a theta-join. R c S c R S   ( ) (sid) sname rating age (sid) bid day 22 dustin 7 45.0 58 103 11/12/96 31 lubber 8 55.5 58 103 11/12/96 S R S sid R sid 1 1 1 1  . .
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  JOIN  Equi-Join: Aspecial case of condition join where the condition c contains only equalities.  Result schema similar to cross-product, but only one copy of fields for which equality is specified.  Natural Join: Equijoin on all common fields. sid sname rating age bid day 22 dustin 7 45.0 101 10/10/96 58 rusty 10 35.0 103 11/12/96 S R sid 1 1
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  PROPERTIES OF JOIN Selecting power: can join be used for selection?  Is join commutative? = ?  Is join associative?  Join and projection perform complementary functions  Lossless and lossy decomposition 11 RS  11 SR  ?1)11()11(1 CRSCRS  
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  DIVISION  Not supportedas a primitive operator, but useful for expressing queries like: Find sailors who have reserved all boats.  Let A have 2 fields, x and y; B have only field y:  A/B =  i.e., A/B contains all x tuples (sailors) such that for every y tuple (boat) in B, there is an xy tuple in A.  Or: If the set of y values (boats) associated with an x value (sailor) in A contains all y values in B, the x value is in A/B.  In general, x and y can be any lists of fields; y is the list of fields in B, and x y is the list of fields of A.  x x y A y B| ,    
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  EXAMPLES OF DIVISIONA/B sno pno s1 p1 s1 p2 s1 p3 s1 p4 s2 p1 s2 p2 s3 p2 s4 p2 s4 p4 pno p2 pno p2 p4 pno p1 p2 p4 sno s1 s2 s3 s4 sno s1 s4 sno s1 A B1 B2 B3 A/B1 A/B2 A/B3
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  EXAMPLE OF DIVISION Find all customers who have an account at all branches located in Chville  Branch (bname, assets, bcity)  Account (bname, acct#, cname, balance)
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  EXAMPLE OF DIVISION R1:Find all branches in Chville R2: Find (bname, cname) pair from Account R3: Customers in r2 with every branch name in r1 123 )(2 )(1 , '' rrr Accountr r cnamebname Branch Chvillebcitybname      
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  EXPRESSING A/B USINGBASIC OPERATORS  Division is not essential op; just a useful shorthand.  Also true of joins, but joins are so common that systems implement joins specially.  Idea: For A/B, compute all x values that are not `disqualified’ by some y value in B.  x value is disqualified if by attaching y value from B, we obtain an xy tuple that is not in A. Disqualified x values: A/B: )))((( ABAxx   x A( )  all disqualified tuples
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  SUMMARY OF RELATIONALALGEBRA  The relational model has rigorously defined query languages that are simple and powerful.  Relational algebra is more operational; useful as internal representation for query evaluation plans.  Several ways of expressing a given query; a query optimizer should choose the most efficient version.