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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. OUTLINE. ECR data model Attribute Equivalence Object Equivalence Strategies for Attribute Integration.
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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
OUTLINE • ECR data model • Attribute Equivalence • Object Equivalence • Strategies for Attribute Integration
ATTRIBUTE EQUIVALENCE • Characteristics of Attributes • Uniqueness • Cardinality • Domain • Static Semantic Integrity Constraints • Dynamic Semantic Integrity Constraints • Security Constraints • Allowable Operations • Scale
Basic Attribute Equivalence Properties • Definition(1)(Basic Equivalence Properties): Let a i attribute of object class A , bi attribute of object class B Di largest non-null subset of DOM(a i ) Ri largest non-null subset of DOM(b i ) such that there exists a mapping function fi : Dig Ri and its inverse. The properties of f i are the follows: • f i is an isomorphism • Each allowable operation on a i has an equivalent allowable operation on b i and vice versa. • All semantic integrity constraints hold under f i and its inverse. • All state change constrains hold under the f i and its inverse • All security constrains hold under the f i and its inverse • f i and its inverse preserve functional dependencies • The mapping functions preserve unique identifiers
Example: Let f1 : D1 R1 Where D1= DOM (social-security-number) R1=DOM (employee-number) f1 (111-11-1111)=1 f1 (222-22-2222)=2 f1 (333-33-3333)=3 f1 (444-44-4444)=4 f1 (555-55-5555)=5 Let f2 :D2 R2 Where D2= DOM (height-in-inches) R2=DOM (height-in-centimeters) f2(x)=2.54*x Let f3: D3 R3 Where D3= DOM (degree) MINUS {1} R3=DOM (education) Minus {MD}) f3 (1)=not defined f3(2)=BS f3 (3)=MS f3 (4)=PhD
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
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, ora STRONG CONTAINS b holds, then a STRONG CONTAINS b • If either a STRONG EQUAL b, ora STRONG CONTAINED-IN b holds, then a STRONG CONTAINED-IN b • If a STRONG EQUAL b, a STRONG CONTAINS b , ora STRONG CONTAINED-IN b hold at different time instances, then a STRONG OVERLAP b
Example DOM(CR1)={1,2,3,4} DOM(CR2)={Frosh,Soph,Jr,Sr} DOM(CR3)={Frosh,Soph,Jr,Sr,Ms,PhD} DOM(CR4)={Jr,Sr,Ms,PhD} DOM(CR54)={1,2}
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)
Example: 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
Disjoint Attribute Equivalence • Example: 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)
Equivalences Between Two Object Classes The five possible integrations of two objects
Strategies For Attribute Integration Strategy1( Integrate All Nondisjoint Attributes)
Strategy3( Integrate Only Attributes That Are Equal, and indicat Relationships between Nonintegrated Similar Attributes)
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