LAV Mediation

There are two main approached for Mediating in Data Integration

  • GAV Mediation - defining global relations in terms of local
  • LAV Mediation - defining local relations in terms of global


LAV - Local-as-View Mediation

  • local relations are defined as views (queries) over global relations
  • goal: define the global schema in such a way that individual definitions don't change when new data sources are added or old are removed
  • See some notation in Mediator (Data Integration)


LAV Mapping

LAV Mapping

  • mapping $S \subseteq Q$ for some Conjunctive Query $Q(\vec{x}) \leftarrow A_1(\vec{u}_1), \ ..., \ A_k(\vec{u}_k)$ over the global relations
  • this gives loose-coupling between global and local schemas


FOL Semantics:

  • $\forall x_1, ..., x_n \Big[ S(x_1, ..., x_n) \Rightarrow \exists \ y_1, ..., y_m \ : \ A_1(\vec{u}_1) \ \land \ ... \ \land \ A_k(\vec{u}_k) \Big]$
  • $S(x_1, ..., x_n)$ - head of a view
  • $y_1, ..., y_m$ - existential variables
  • $A_1(\vec{u}_1) \ \land \ ... \ \land \ A_k(\vec{u}_k)$ - body


Example

Suppose we have this global schema

  • Student(studentName),
  • EuropeanStudent(studentName),
  • University(uniName),
  • NonEuropeanStudent(studentName),
  • FrenchUniversity(uniName),
  • EuropeanUniversity(uniName),
  • NonEuropeanUniversity(uniName),
  • Program(title),
  • MasterProgram(title),
  • EnrolledInProgram(studentName, title),
  • Course(code),
  • EnrolledInCourse(studentName, code),
  • PartOf(code, title),
  • RegisteredTo(studentName, uniName),
  • OfferedBy(title, uniName).


Data sources from the previous examples

  • S1.Catalogue(nomUniv, programme). - programs in French universities
  • S2.Erasmus(student, course, univ). - European Erasmus students
  • S3.CampusFr(student, program, university). - foreign students in France
  • S4.Mundus(program, course). - international master programs


LAV Mappings:

  • $m_1$: S1.Catalogue(U, P) $\subseteq$ FrenchUniversity(U), Program(P), OfferedBy(P, U), OfferedBy(P', U), MasterProgram(P')
  • $m_2$: S2.Erasmus(S, C, U) $\subseteq$ Student(S), EnrolledInCourse(S, C), PartOf(C, P), OfferedBy(P, U), EuropeanUniversity(U), EuropeanUniversity(U') RegisteredTo(S, U'), U $\neq$ U'
  • $m_3$: S3.CampusFr(S, P, U) $\subseteq$ NonEuropeanStudent(S), Program(P), EnrolledInProgram(S, P), OfferedBy(P, U), FrenchUniversity(U), RegisteredTo(S, U)
  • $m_4$: S4.Mundus(P, C) $\subseteq$ MasterProgram(P), OfferedBy(P, U), OfferedBy(P, U'), EuropeanUniversity(U), NonEuropeanUniversity(U'), PartOf(C, P)


So,

  • LAV mapping can be seen as a description of the data source in terms of the global schema
  • for example, Erasmus students ($m_2$) are
    • European students
    • enrolled in an European university
    • that European university is different from their home university
    • they remain registered in their home university

Loose-Coupling

  • This gives loose-coupling between local and global relations
  • which is important when participating data sources change frequently


Query Answering

suppose we're interested in Master students

  • define the following query
  • $\text{MasterStudent}(E) \leftarrow \text{Student}(E), \text{EnrolledInProgram}(E, M), \text{MasterProgram}(M).$
  • how to find which data sources to query?
  • rewriting process is more complex, than for GAV

Algorithms to do that


Sources