CS246

1
CS246

• Query Translation

2
Mind Your Vocabulary

• Q What is the problem?
• A How to integrate heterogeneous sources when
  their schema capability are different

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Bestbookbuys.com

• How to integrate?

Mediator
fn Tom ln Clancy
au Clancy, Tom
Amazon.com
bn.com
4
Framework

• User expresses a query using a mediator schema
• Mediator translates the query to source-supported
  queries
• Mediator collects and postprocess results from
  the sources

fn Tom ln Clancy
Mediator
fn Tom ln Clancy
au Clancy, Tom
Amazon.com
bn.com
5
Difference From Previous Studies?

• Heterogeneous attributes
• Different vocabularies
• Semantic translation necessary
• Previous studies assumed homogeneous attributes
  for all sources
• Complex Boolean queries
• Not just conjunctive queries

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Main Challenge

• How to best translate a query when the mediator
  and the source use different model/schema?
• Author ? lastname, firstname
• Western calendar ? Chinese lunar calendar

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Query Translation Example

• Q For the above schema, best translation for
  last Clancy year 1998 month
  Jan?
• A author Clancy date winter, 1998?

8
More Translation Examples

• More translations for the same schemas
• publisher p last l first f?
  publisher p author l, f
• title t last l first f? title
  t author l, f
• Do we have to translate every possible query
  manually? Is it necessary to have separate rules
  for the above translations? Can the system
  automatically translate queries?
• Any idea?

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Observations

• The system cannot figure out last l first
  f ? author l, f
• No semantic knowledge
• User needs to provide these types of mappings
• There seem to exist basic mappings
• However, system may compose correct translation
  using basic translations
• last l first f ? author l, f
• year yy month Jan ? date spring,
  yy

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Framework
Mediator Context
Source Context

• Human expert provides a set of basic rules
• last l first f ? author l, f
• year yy month Jan ? date spring,
  yy

Basic rules
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Framework

• Given a query, the system automatically
  translates the query using the basic rules

Basic rules
Qm First Tom Last Clancy
Qs Author Clancy, Tom
Traslation Algorithm
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Advantage of the Proposed Framework

• Minimizes manual intervention
• Human input only for the initial rule writing
• Can translate any queries
• Not just template queries

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Questions

• How do we know whether a translation is good or
  correct?
• What basic rules are necessary?
• Do we need a rule for last l first f?
• How do we translate?
• Algorithm for good translation?

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Good Translation?

• Q Why do we think these are good translations?
• last Clancy first Tom ? author
  Clancy, Tom
• year 2002 month Jan? date
  winter, 2002
• A Results for the translated queries are close
  to the original queries

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Minimal Subsuming (or Containing) Translation

• Definition of closeness in the paper
• Q original query ? S(Q) translated query
• We also use Q and S(Q) to represent results
• S(Q) minimal superset of Q expressed in the
  source terms

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Minimal Subsuming Translation

• Find the minimal subsuming translation from the
  original query
• Filter out false positives by applying
  filtering condition at the mediator

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Any Alternative for Closeness?

• What about maximal subsumed translation?
• Definition of previous studies
• Maybe a good definition when result is large or
  filtering is impossible

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Any Alternative for Closeness?

• Consider both false positives and false
  negatives Maximize S(Q)?Q / S(Q)?Q
• Other definitions possible depending on scenario

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Questions

• How do we know whether a translation is good or
  correct?
• Minimal subsuming translation
• What basic rules are necessary?
• Do we need a rule for last l first f?
• How do we translate?
• Algorithm for good translation?

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Three Main Concepts

• Query Separability
• Query Safety
• Cross matching

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Query Separability

• Q ln Clancy fn Tom p
  Wiley
• We still get minimal subsuming translation if we
  separately translate
• ln Clancy fn Tom and p Wiley
• Q C1 ? C2 ? C3 (? or ) is separable if
  S(Q) S(C1) ? S(C2) ? S(C3)

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Disjunction Separability Theorem CGM96

• Disjunctions are always separable
• Q C1 C2 C3 ? S(Q) S(C1) S(C2)
  S(C3)for any C1, C2 and C3
• Assuming minimal subsuming translation semantics
• Implication
• Basic rules are necessary only for conjunctions
• e.g., c1 c2, but not c1 c2
• Why?
• Any complex queries can be transformed to DNF
• Significant simplification for a rule writer

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Basic Rules

• Simple conjunction of constraints
• Separability of conjunctions is determined by a
  human expert
• ln fn but not ln publisher
• User-provided basic rules are assumed to be sound
  and complete
• Soundness All mappings are correct (minimal
  subsuming translation)
• Completeness Contains all inseparable simple
  conjunctions

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Questions

• How do we know whether a translation is good or
  correct?
• What basic rules are necessary?
• Do we need a rule for last l first f?
• How do we translate?
• Algorithm for good translation?

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Translation Algorithm

• Simple conjunction query
• Step 1 Find all matching rules

Q
Rules

ln l ? au l ln l fn f ? au
l, f p p ? p p
ln l
fn f
p p
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Translation Algorithm

• Simple conjunction query
• Step 2 Remove subset matching
• Superset matching is more precise

Q
Rules

ln l ? au l ln l fn f ? au
l, f p p ? p p
ln l
fn f
p p
au l
au l, f
p p
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Translation Algorithm

• Simple conjunction query
• Step 3 Generate translated query

Q
Rules

ln l ? au l ln l fn f ? au
l, f p p ? p p
ln l
fn f
p p

au l, f
p p
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Translation Algorithm

• Complex Boolean query?

Q


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Solution 1 (Algorithm DNF)

• Convert to DNF and translate
• Disjunctions are always separable
• We can individually translate each
  disjunct

Q
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Whats Wrong with DNF?

• DNF conversion is exponential
• DNF parse tree is not compact
• Global conversion often not necessary
• Translation of C3 is independent of others

C1
C2
C3
p ... independent

x fn
y fn
z ln ...
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Conjunction Partitioning

• Partition conjuncts into independent groups
• Translate each group separately
• By rewriting local groups
• Top level AND of C3 is preserved.

C1
C2
C3
p ... independent

x fn
y fn
z ln ...
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Independent Groups?

• Q How do we know G1 and G2 are independent?
• A Q G1 G2 is separable
• Q How do we know Q G1 G2 is separable?

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Safety Condition

• Query seperability is difficult to check directly
• Safety condition A practical way to check query
  separability
• Sufficient condition for query separability
• But not a necessary condition

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Safety Condition for Simple Conjunction

• M(Q) Matching rules for Q
• Q G1 G2
• G1 and G2 are simple conjunction
• G1 C1 C2, G2 C3 C4
• Q is safe iff M(Q) M(G1) ? M(G2)
• That is, Q is safe if there is no cross
  matching among G1 and G2
• Cross matching a rule that matches some
  constraints in G1 and some constraints in G2
• Example
• G1 fnf1 fn f2, G2 ln ln
• Q G1 G2 unsafe cross matching of fn ln ?
  au

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Safety Condition for Complex Disjunction

• M(Q) Matching rules for Q
• Q G1 G2
• G1 and G2 are complex disjunction
• G1 C1 C2, G2 C3 C4
• Disjuntivize Q Q C1 C3 C1 C4
  C2 C3 C2 C4
• Q is safe iff every disjunct is safe i.e., if
  all C1 C3, C1 C4, C2 C3, and C2
  C4 are safe

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Important Theorem

• A query is separable if it is safe (i.e., query
  separability ? safety)
• A query is safe if there is no cross
  matching(i.e., safety ? no cross matching)
• If there is a cross-matching between conjuncts,
  we cannot separately translate them
• Put them into the same group

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Algorithm TDQM

• Recursively traverse the query tree in the
  top-down order
• At a disjunction node
• Separately translate its children
• At a conjunction node
• Put the children with cross matching into the
  same group and rewrite the query locally in each
  group

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Algorithm TDQM



xfn
yfn
zln ...
vp ...
wy ...
Recursively traverse the tree top-down

• At a disjunction node
• Separately apply TDQM each child
• Disjunction separability theorem

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Algorithm TDQM



xfn
yfn
zln ...
vp ...
wy ...

• At a conjunction node
• Group children by identifying cross-matchings
• No cross-matching between groups (safety
  condition)

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Algorithm TDQM

wy ...

• For groups with more than one conjunct
• Locally rewrite into a disjunctive form (not DNF)

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Algorithm TDQM

wy ...

• For groups with more than one conjunct
• Locally rewrite into a disjunctive form (not DNF)

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Algorithm TDQM





wy ...
vp ...
x
z
y
z

• Continue tree traversal until we reach simple
  conjunction and apply basic mappings

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Algorithm TDQM

• Generates minimal subsuming translation
• Resulting translation is compact
• Assuming the original query is compact
• Convert the tree only when it is necessary

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TDQM Summary

• Key conceptsSeperability ? Safety ?? cross
  matching
• Local rewriting for compact translation

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A Few Remarks

• Final algorithm is straightforward
• Simply put, separately translate each term if
  there is no cross-matching
• Many people can come up with the algorithm
• But the author developed an amazing theory by
  carefully studying basic questions
• Initial problem looks rather trivial
• But a mine-field of interesting research topics

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Questions?