A theory of Attribute Equivalence in Databases with Application to Schema 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

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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 , 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 Di g
  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

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Example
Let f1 D1 ? R1 Where D1 DOM
(social-security-number) R1DOM
(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) R2DOM (height-in-centimete
rs) f2(x)2.54x  
 
Let f3 D3 ? R3 Where D3 DOM (degree)
MINUS 1 R3DOM (education) Minus MD)
f3 (1)not defined f3(2)BS f3 (3)MS f3
(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
  fD? 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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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
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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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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(Sophomor
e)f(Jr)f(Sr)undergrad f(MS)
(PhD)grad     is CR3 WEAK ? EQUAL CR6
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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)
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? Equivalences Between Two Object Classes
The five possible integrations of two objects
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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