Semantic Adaptation of Schema Mappings when Schemas Evolve

1
Semantic Adaptation of Schema Mappings when
Schemas Evolve

• Cong Yu
• University of Michigan
• Lucian Popa
• IBM Almaden Research Center

VLDB05, Trondheim, Norway Sep 2, 2005
2
Schema Mappings
?
Schema S
Schema T
J
I
q
q

• Schema Mappings are logical, declarative,
  assertions that can describe relationships
  between schemas.
• enough semantics to guide run-time,
  instance-level, transformation
• e.g., GLAV mappings (or tuple-generating
  dependencies)
• They are key elements in two main areas in
  information integration
• Data Exchange/Translation
• Query Answering/Rewriting (or Federation)

3
Schema Evolution and Mapping Adaptation

• Schemas evolve over time Mappings may become
  invalid !
• A lot of effort goes into establishing mappings.
  How do we reuse them ?
• Mapping Adaptation Problem VMP03
• Given
• mapping M from S to T,
• changes/evolution of S to S, or T to T, or
  both,
• Derive a best mapping M that
• is valid with respect to the new schemas, and
• reflects the original mapping as much as possible
  

4
Prior Solution Incremental Method
M
move elem
S
T
M1
add elem
T1
M2
T2
delete constraint
M3
T3
rename elem

• VMP03 Incrementally adapts the mapping after
  each atomic change in the schemas (source and/or
  target).
• Efficient and intuitive, for one or few changes.
• However, for non-incremental evolution, there are
  drawbacks

5
M
T
S
Different evolution paths
Mn
Tn

• The new schema may be radically different
• The list of changes may not be known.
• Evolution path must be discovered ? not
  necessarily unique
• The method will ultimately be inefficient
• The algorithm must be applied at each atomic
  change
• As we shall see, the resulting mapping may not be
  the expected one.

6
Our Approach Composition-Based
M
S
Can use schema mapping tools (e.g., Clio) to
construct E.
T
E
M M E
T

• Evolution itself is described as a schema
  mapping.
• Concise, declarative, and expressive description
  of evolution.
• Enables efficiency and can deal with arbitrary
  evolution
• The adapted mapping is then obtained via
  composition.
• Formal semantics of adaptation.
• At high level, this is part of the model
  management vision Ber03.

7
Main Contributions

• We study the interplay between schema evolution
  and mapping composition
• interesting in terms of both semantics and
  implementation
• We show that the composition-based approach for
  mapping adaptation can be practical

8
Outline of the Rest of the Talk

• Incremental Approach vs. Composition Approach
• Example (showing why composition is important)
• Composition Semantics and Algorithm
• Transformation semantics
• ? specialized, more suitable for schema
  evolution, also more challenging
• Optimization and Experiments
• Compose only when necessary
• (Some mapping formulas are unaffected by the
  change)
• Conclusion

9
Simplified Example
Source
Source
Target

• m SuppPart (s, p) ? PartOrder (p, o)
• ? PotentialSupp (s, o)
• ( GLAV mapping Halevy01, or,
• source-to-target tgd FKMP03 )

SuppPart
LineItem
m
s p
PotentialSupp
li s p o qty
s o
PartOrder
p o

• The mapping m exports orders o and all their
  potential suppliers s.
• Schema evolution scenario
• Data arrives in long tuples, each relating an
  order, a part and an available supplier.
• The mapping m must be adapted to use new schema
  Source.

10
Incremental Approach VMP03
Source
Target
Source
m SuppPart (s, p) ? PartOrder (p, o)
? PotentialSupp (s, o)
SuppPart
LineItem
m
s p
PotentialSupp
li s p o qty
s o
PartOrder
p o

• Pick a list of changes from Source to Source and
  rewrite mapping after each change.
• (1) Move element SuppPart/s to PartOrder/s
• SuppPart (p) ? PartOrder (s, p, o) ?
  PotentialSupp (s, o)
• (2) Delete SuppPart/p and (3) delete SuppPart.
• (4) Rename PartOrder to LineItem, (5) add
  LineItem/li and (6) add LineItem/qty
• m LineItem (li, s, p, o, qty) ?
  PotentialSupp (s, o)

11

• Although small, our example already needs 6
  schema changes.
• For large schemas, this can become challenging
• Furthermore, and somewhat surprisingly, the
  semantics of the adapted mapping may not be the
  expected one !

12
Loss of Semantics
Source
Target
Source
m SuppPart (s, p) ? PartOrder (p, o)
? PotentialSupp (s, o)
SuppPart
LineItem
m
s p
PotentialSupp
li s p o qty
m LineItem (li, s, p, o, qty) ?
PotentialSupp (s, o)
s o
PartOrder
p o

• The original mapping m joins orders with
  suppliers
• However, m loses relevant suppliers
• It only pairs an order with a supplier provided
  they appear in the same LineItem tuple
• To retain the original semantics, we must look in
  different tuples !
• m LineItem (li, s, p, o, qty) ?
  LineItem (li, s, p, o, qty)
• ?
  PotentialSupp (s, o)

13

• The incremental approach is a mechanical
  procedure that makes local changes to the
  mapping.
• A sequence of good local changes may not
  necessarily yield the best global adaptation

14
Mapping Composition Approach

• We look at the evolution globally
• Describe evolution through a schema mapping
  Source ? Source.

Source
Target
Source
SuppPart
LineItem
m
e1
s p
PotentialSupp
e1 LineItem (l, s, p, o, q) -gt SuppPart (s, p)
e2 LineItem (l, s, p, o, q) -gt PartOrder (p, o)
li s p o qty
s o
PartOrder
p o
e2

• Define the adapted mapping to be a mapping
  Source ? Target, equivalent (e.g., same data
  movement) to the sequence of the evolution
  mapping and the original mapping.
• The previous m satisfies the conditions for
  e1,e2 and m.

15

• The composition approach is a more systematic
  approach, with precise semantics, guaranteed to
  behave the right way in all situations.
• Although it may appear simple in the previous
  example, mapping composition poses challenges

16
Challenges in Composition Approach

• Mapping language
• Must handle nesting and complex types (as in XML
  Schema)
• (details in the paper)
• Furthermore, the usual mapping languages (GLAV,
  tuple-generating dependencies) are not closed
  under composition !
• Recent extension that ensures composability
  second-order tgds FKPT04.
• Main idea add functions to gain needed
  expressive power
• Semantics and Algorithm
• Efficiency/Scalability

Next
17
Composition Semantics and Algorithm
18
Composition Semantics

• In mapping composition, we want to replace a
  sequence of schema mappings with one that is
  equivalent and avoids the middle schema.
• What does equivalent mean ?
• There are two semantics that we considered
• Relationship semantics
• More general
• Transformation semantics
• More suitable, specialized

19
Relationship Semantics

• Mappings can be viewed as describing
  relationships between instances over the two
  schemas
• Rel (M12) (I1, I2) (I1, I2) satisfies M12
  
• Composition of relationships
• Rel (M12) ? Rel (M23) (I1, I3) there is
  I2 such that
• (I1,
  I2) satisfies M12 and (I2, I3) satisfies M23
• FKPT04, Melnik04 A mapping M13 is equivalent,
  to the sequence of M12 and M23, under the
  relationship semantics, if
• Rel (M13) Rel (M12) ? Rel (M23)

20
Example Semantics and Algorithm
S3
S1
S2
Unknown student id (Skolem term)
Student
Second-order tgd FKPT04
E
Takes
sid name
M
Takes
sid name course
M Takes (n, c) ? Student (F(n), n)
? Enrolls (F(n), c) E Student (s,
n) ? Enrolls (s, c) ?
Takes (s, n, c)
name course
Enrolls
sid course

• M13 correctly captures the equivalent
  relationship between instances of S1 and S3.
• Instances (and function F) can exist a priori.
• A student n must be paired with a course c
• even when c is listed under a different student
  name n,
• provided the student id is the same F(n)
  F(n)

1. Substitution
M13 Takes (n, c) ? Takes (n, c) ? F(n)
F(n) ? Takes (F(n), n, c)
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• However, if we assume that the function F is
  one-to-one, an important simplification can be
  made

M13 Takes (n, c) ? Takes (n, c) ?
Takes (F(n), n, c)
M13 Takes (n, c) ? Takes (n, c) ? F(n)
F(n) ? Takes (F(n), n, c)
2. Reduction
F(n) F(n) ? n n
3. Minimization
Equivalent relationship
M13 Takes (n, c) ? Takes (F(n), n,
c)
Equivalent transformation

• We can always make this assumption, if mappings
  are meant to describe transformations (i.e.,
  generation of a target instance).
• F is a Skolem function assigning unique student
  ids n ? F(n)

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Transformation Semantics

• A mapping is a process (in the spirit of data
  exchange FKMP03)
• I2 M12(I1)
• Each mapping formula is a generator of target
  facts
• Functions are one-to-one value generators
• Theorem. Our composition algorithm produces the
  schema mapping with the equivalent transformation
  semantics
• M13 (I1) M23( M12(I1) ) (up to
  the renaming of nulls)
• Advantage of transformation semantics, in
  adaptation
• ? simpler and more intuitive formulas !

23
Composition Algorithm Further Details

• The substitution step is more complex than shown
  
• Must handle nesting
• Generate parameterized rules for set types in the
  middle schema
• Reuse some of the mapping-based query rewriting
  techniques YP04
• Minimization
• Good it simplifies formulas and generates
  intuitive mapping.
• (all this is enabled by the transformation
  semantics)
• Bad it can be expensive (same as tableau
  minimization)

24
Optimization and Experimental Results
25
Full Adaptation

• Full adaptation ? Compose whole schema mappings
  
• (Compose all the formulas in the original
  mapping with all the formulas in the evolution
  mapping)
• Inevitable when the schema evolution is drastic
  and affects most of the original mapping
  (non-incremental evolution)
• Inefficient when the changes are small and
  localized (incremental evolution)

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Compose Only When Necessary

• Mapping Pruning
• 1. Detect those parts (formulas) Mo of the
  original mapping Mo that are affected by
  evolution.
• Only Mo need to be adapted.
• 2. Only a subset Me of the formulas in the
  evolution mapping Me play a role in the
  composition with Mo
• The rest are redundant (PTIME containment-like
  analysis, see paper)
• 3. Compose Mo with Me
• ? Big performance gain for incremental evolution
  and overall.

27
Analysis of Evolution Scenarios
Results based on Clio
Benefits 1 adapted mappings / (blank-sheet
mappings missed mappings)
We also have synthetic scenarios that show
scalability of Mapping Pruning with increasing
schema and mapping complexity
28
Conclusion

• We studied
• Mapping composition techniques for mapping
  adaptation
• Transformation semantics in the context of schema
  evolution
• Designed and implemented a practical adaptation
  system
• Mapping pruning (schema evolution specific)
• To Do
• Optimization of composition in general
• Improve performance of minimization