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A theory of Attribute Equivalence in Databases with Application to Schema Integration

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

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  1. 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

  2. OUTLINE • ECR data model • Attribute Equivalence • Object Equivalence • Strategies for Attribute Integration

  3. THE ECR MODEL OF DATA

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

  5. Example: ATTRIBUTE CHARACTERISTIC

  6. 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

  7. 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

  8. 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

  9. Example:

  10. 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

  11. 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}

  12. 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)

  13. 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

  14. 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)

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

  16. Strategies For Attribute Integration Strategy1( Integrate All Nondisjoint Attributes)

  17. Strategy2( Integrate Only Attributes That Are  Equal)

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

  19. 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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