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, 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

7. 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 (111-11-1111)=1 f 1 (222-22-2222)=2 f 1 (333-33-3333)=3 f 1 (444-44-4444)=4 f 1 (555-55-5555)=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

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, 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

11. 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

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. 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:

14. 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

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

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