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A theory of Attribute Equivalence in Databases with Application to Schema Integration JAMES A.LARSON SHAMKANT B. NAVATHE RAMEZ ELMASRI Presented by REEMA AL-KAMHA

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OUTLINE ECR data model Attribute Equivalence Object Equivalence Strategies for Attribute Integration

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THE ECR MODEL OF DATA

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ATTRIBUTE EQUIVALENCE Characteristics of Attributes –Uniqueness –Cardinality –Domain –Static Semantic Integrity Constraints –Dynamic Semantic Integrity Constraints –Security Constraints –Allowable Operations –Scale

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Example: ATTRIBUTE CHARACTERISTIC

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Basic Attribute Equivalence Properties Definition(1)(Basic Equivalence Properties): Let a i attribute of object class A, b i attribute of object class B D i largest non-null subset of DOM(a i ) R i largest non-null subset of DOM(b i ) such that there exists a mapping function f i : D i R i and its inverse. The properties of f i are the follows: 1)f i is an isomorphism 2)Each allowable operation on a i has an equivalent allowable operation on b i and vice versa. 3)All semantic integrity constraints hold under f i and its inverse. 4)All state change constrains hold under the f i and its inverse 5)All security constrains hold under the f i and its inverse 6)f i and its inverse preserve functional dependencies 7)The mapping functions preserve unique identifiers

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Let f 2 : D 2 R 2 Where D 2 = DOM (height-in-inches) R 2 =DOM (height-in-centimeters) f 2 (x)=2.54*x Let f 1 : D 1 R 1 Where D 1 = DOM (social-security-number) R 1 =DOM (employee-number) f 1 ( )=1 f 1 ( )=2 f 1 ( )=3 f 1 ( )=4 f 1 ( )=5 Example: Let f 3 : D 3 R 3 Where D 3 = DOM (degree) MINUS {1} R 3 =DOM (education) Minus {MD}) f 3 (1)=not defined f 3 (2)=BS f 3 (3)=MS f 3 (4)=PhD

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Strong Attribute Equivalence Definition (STRONG Equivalence) :Given an attribute a of object class A, and attribute b of object class B at some point in time, and f:D R : –If a and b obey the Basic Equivalence Properties of the definition(1), D = VALUES(a) and R = VALUES(b) then a STRONG EQUAL b –If a and b obey the Basic Equivalence Properties of the definition(1), and D = VALUES(a), R VALUES(b) then a STRONG CONTAINS –If a and b obey the Basic Equivalence Properties of the definition(1), D VALUES(a), R = VALUES(b) then a STRONG CONTAINED-IN b –If a and b obey the Basic Equivalence Properties of the definition(1) and D VALUES(a), R VALUES(b),then a STRONG OVERLAPS b

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Example:

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Strong Attribute Equivalence Definition (STRONG Equivalences) :Let a be an attribute of class A, and b be an attribute of class B then: –If a STRONG EQUAL b holds, then a STRONG EQUAL b –If either a STRONG EQUAL b, or a STRONG CONTAINS b holds, then a STRONG CONTAINS b –If either a STRONG EQUAL b, or a STRONG CONTAINED-IN b holds, then a STRONG CONTAINED-IN b –If a STRONG EQUAL b, a STRONG CONTAINS b, or a STRONG CONTAINED-IN b hold at different time instances, then a STRONG OVERLAP b

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DOM(CR 1 )={1,2,3,4} DOM(CR 2 )={Frosh,Soph,Jr,Sr} DOM(CR 3 )={Frosh,Soph,Jr,Sr,Ms,PhD} DOM(CR 4 )={Jr,Sr,Ms,PhD} DOM(CR5 4 )={1,2} Example

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Weak Attribute Equivalence Definition :Attributes a and b are Weak equivalent if all conditions of STRONG equivalence hold with the following exceptions: a) No inverse function need exist b) The properties 3,4,5 of definition1 are changed as follows: - Each constraint in SIC(a) should hold in SIC(b) -Each constraint in SCC(a), and SEC(a) hold in SCC(b) and SEC(b)

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Given DOM(CR3)={Freshman,Sophomore,Jr,Sr,Ms,PhD} DOM(CR6)={undergrad,grad} The function f that maps CR3 to CR6 where: f(Freshman)=f(Sophomore)=f(Jr)=f(Sr)=undergrad f(MS)= (PhD)=grad is CR3 WEAK EQUAL CR6 Example:

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Let DOM(CR7)={Freshman,Sophomore,Jr,Sr} DOM(CR8)={Ms,PhD} New attribute CR9 can be generated where: DOM(CR9)= DOM(CR7) UNION DOM(CR8) Disjoint Attribute Equivalence

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The five possible integrations of two objects Equivalences Between Two Object Classes

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Strategies For Attribute Integration Strategy1( Integrate All Nondisjoint Attributes)

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Strategy2( Integrate Only Attributes That Are Equal)

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Strategy3( Integrate Only Attributes That Are Equal, and indicat Relationships between Nonintegrated Similar Attributes)

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Conclusion Attribute equivalence solve many traditional schema integration problems: –Naming Conflicts –Scale Difference –Difference in Level of Abstraction of Attributes –Difference in Object Identifiers –Difference in Representation

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