CSE 636 Data Integration

1
CSE 636Data Integration

• Answering Queries Using Views
• Bucket Algorithm

2
The Bucket Algorithm

• Each subgoal g of Q must be covered by some
  view
• Make a list of candidates (buckets) per query
  subgoal
• Consider combinations of candidates from
  different buckets
• Not all combos are compatible
• Keep the compatible ones and minimize them
• Discard the ones contained in another
• Take their union

3
The Bucket Algorithm

• q(X,Y,R) - ForSale(X,Y,C,auto),
  Review(X,R,auto),
• Y gt 1985
• Step 1 For each subgoal, put the relevant
  sources into a bucket
• V1(name, year) - ForSale(name, year, France,
  auto),
• year gt 1990 would be
  relevant
• V3(name, year) - ForSale(name, year, France,
  cheese)
• would be irrelevant
• Step 2 Take the Cartesian product of the buckets
• Algorithm produces maximally contained rewriting
• Ignores interactions between subgoals in Step 1

4
The Bucket Algorithm Example

• V1(Std,Crs,Qtr,Title) - reg(Std,Crs,Qtr),
  course(Crs,Title),
• Crs 500, Qtr
  Aut98
• V2(Std,Prof,Crs,Qtr) - reg(Std,Crs,Qtr),
  teaches(Prof,Crs,Qtr)
• V3(Std,Crs) - reg(Std,Crs,Qtr), Qtr Aut94
• V4(Prof,Crs,Title,Qtr) - reg(Std,Crs,Qtr),
  course(Crs,Title),
• 
  teaches(Prof,Crs,Qtr), Qtr Aut97
• q(S,C,P) - teaches(P,C,Q), reg(S,C,Q),
  course(C,T),
• C 300, Q Aut95
• Step 1 For each query subgoal, put the relevant
  sources into a bucket

5
The Bucket Algorithm Example

• V1(Std,Crs,Qtr,Title) - reg(Std,Crs,Qtr),
  course(Crs,Title),
• Crs 500, Qtr
  Aut98
• V2(Std,Prof,Crs,Qtr) - reg(Std,Crs,Qtr),
  teaches(Prof,Crs,Qtr)
• V3(Std,Crs) - reg(Std,Crs,Qtr), Qtr Aut94
• V4(Prof,Crs,Title,Qtr) - reg(Std,Crs,Qtr),
  course(Crs,Title),
• 
  teaches(Prof,Crs,Qtr), Qtr Aut97
• q(S,C,P) - teaches(P,C,Q), reg(S,C,Q),
  course(C,T),
• C 300, Q Aut95
• P?Prof, C?Crs, Q?Qtr
• Note Arithmetic predicates dont pose a problem

Buckets
teaches
reg
course
V2
V4
6
The Bucket Algorithm Example

• V1(Std,Crs,Qtr,Title) - reg(Std,Crs,Qtr),
  course(Crs,Title),
• Crs 500, Qtr
  Aut98
• V2(Std,Prof,Crs,Qtr) - reg(Std,Crs,Qtr),
  teaches(Prof,Crs,Qtr)
• V3(Std,Crs) - reg(Std,Crs,Qtr), Qtr Aut94
• V4(Prof,Crs,Title,Qtr) - reg(Std,Crs,Qtr),
  course(Crs,Title),
• 
  teaches(Prof,Crs,Qtr), Qtr Aut97
• q(S,C,P) - teaches(P,C,Q), reg(S,C,Q),
  course(C,T),
• C 300, Q Aut95
• S?Std, C?Crs, Q?Qtr
• Note V3 doesnt work arithmetic predicates not
  consistent
• V4 doesnt work S not in the output of V4

Buckets
teaches
reg
course
V2
V1
V4
V2
7
The Bucket Algorithm Example

• V1(Std,Crs,Qtr,Title) - reg(Std,Crs,Qtr),
  course(Crs,Title),
• Crs 500, Qtr
  Aut98
• V2(Std,Prof,Crs,Qtr) - reg(Std,Crs,Qtr),
  teaches(Prof,Crs,Qtr)
• V3(Std,Crs) - reg(Std,Crs,Qtr), Qtr Aut94
• V4(Prof,Crs,Title,Qtr) - reg(Std,Crs,Qtr),
  course(Crs,Title),
• 
  teaches(Prof,Crs,Qtr), Qtr Aut97
• q(S,C,P) - teaches(P,C,Q), reg(S,C,Q),
  course(C,T),
• C 300, Q Aut95
• C?Crs, T?Title

Buckets
teaches
reg
course
V2
V1
V1
V4
V2
V4
8
The Bucket Algorithm Example

• Step 2
• Try all combos of views, one each from a bucket
• Test satisfaction of arithmetic predicates in
  each case
• e.g., two views may not overlap, i.e., they may
  be inconsistent
• Desired rewriting union of surviving ones
• Query rewriting 1
• q1(S,C,P) - V2(S,P,C,Q), V1(S,C,Q,T),
  V1(S,C,Q,T)
• no problem from arithmetic predicates (none in
  V2)
• May or may not be minimal (why?)

teaches
reg
course
V2
V1
V1
V4
V2
V4
9
The Bucket Algorithm Example

• Unfolding of rewriting 1
• q1(S,C,P) - r(S,C,Q), t(P,C,Q), r(S,C,Q),
  c(C,T), r(S,C,Q),
• c(C,T), C 500, Q Aut98, C
  500, Q Aut98
• Black rs can be mapped to green r S?S, S?S,
  Q?Q
• Black c can be mapped to green c just extend
  above mapping to T?T
• Minimized unfolding of rewriting 1
• q1m(S,C,P) - t(P,C,Q), r(S,C,Q), c(C,T), C
  500, Q Aut98
• Minimized rewriting 1
• q1m(S,C,P) - V2(S,P,C,Q), V1(S,C,Q,T)

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The Bucket Algorithm Example
teaches
reg
course

• Query Rewriting 2
• q2(S,C,P) - V2(S,P,C,Q), V1(S,C,Q,T),
  V4(P,C,T,Q)
• q2(S,C,P) - r(S,C,Q), t(P,C,Q), r(S,C,Q),
• r(S,C,Q), c(C,T), C 500, Q
  Aut98,
• r(S,C,Q), c(C,T),
  t(P,C,Q), Q Aut97
• This combo is infeasible consider the
  conjunction of arithmetic predicates in V1 and V4
• Query rewriting 3
• q3(S,C,P) - V2(S,P,C,Q), V2(S,P,C,Q),
  V4(P,C,T,Q)

V2
V1
V1
V4
V2
V4
teaches
reg
course
V2
V1
V1
V4
V2
V4
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The Bucket Algorithm Example

• Unfolding of rewriting 3
• q3(S,C,P) - r(S,C,Q), t(P,C,Q), r(S,C,Q),
  t(P,C,Q), r(S,C,Q),
• c(C,T), t(P,C,Q), Q Aut97
• The green subgoals can cover the black ones under
  the mapping S?S, S?S, P?P, P?P, Q?Q
• Minimized rewriting 3
• q3m(S,C,P) - V2(S,P,C,Q), V4(P,C,T,Q)
• Verify that there are only two rewritings that
  are not covered by others
• Maximally Contained Rewriting
• q q1m ? q3m

12
The Bucket Algorithm Example 2

• Query
• q(X) - cites(X,Y), cites(Y,X), sameTopic(X,Y)
• Views
• V4(A) - cites(A,B), cites(B,A)
• V5(C,D) - sameTopic(C,D)
• V6(F,H) - cites(F,G), cites(G,H), sameTopic(F,G)
• Note Should we list V4(X) twice in the buckets?

Buckets
cites
cites
sameTopic
V4
V4
V5
V6
V6
V6
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The Bucket Algorithm Example 2

• Consider all combos check for containment of
  the unfolded rewriting in Q
• V4(X) cannot be combined with anything (why?)
• Try q1(X) - V4(X), V4(X), V5(X,Y)
• Try q2(X) - V4(X), V6(X,Y), V5(X,Y)
• Does any of these work?
• When can we discard a view from consideration?

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The Bucket Algorithm Example 2

• Here is a successful rewriting
• q3(X) - V6(X,Y), V6(X,Y), V6(X,Y)
• By itself is not contained in Q
• But, with subgoal XY added, it is!
• By minimizing the rewriting, we get
• q3m(X,Y) - V6(X,X)

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The Bucket Algorithm Example 2

• Remarks
• V4 didnt contribute to any rewrite, but the
  bucket algorithm doesnt recognize it ahead
• Considerq2(X,Y) - cites(X,Y), cites(Y,X)
• Then both cites predicates can be folded into V4
• Not recognized by the bucket algorithm

16
The State of Affairs

• Bucket algorithm
• deals well with predicates, Cartesian product can
  be large (containment check required for every
  candidate rewriting)
• Inverse rules
• modular (extensible to binding patterns, FDs)
• no treatment of predicates
• resulting rewritings need significant further
  optimization
• Neither scales up
• The MINICON algorithm
• change perspective look at query variables

17
References

• Querying Heterogeneous Information Sources Using
  Source Descriptors
• By Alon Y. Levy, Anand Rajaraman and Joann J.
  Ordille
• VLDB, 1996
• Laks VS Lakshmanan
• Lecture Slides
• Alon Halevy
• Answering Queries Using Views A Survey
• VLDB Journal, 2000
• http//citeseer.ist.psu.edu/halevy00answering.html