1 Data integration Most slides are borrowed from Dr. Chen Li, UC Irvine.

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Data integration

Most slides are borrowed from Dr. Chen Li, UC Irvine

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Motivation

Legacy database Plain text files

Biblio sever

Support seamless access to autonomous and heterogeneous information sources.

http://us.imdb.com/ImageView?u=http://images.amazon.com/images/P/B00003CXXJ.01.LZZZZZZZ.jpg

http://us.imdb.com/ImageView?u=http://images.amazon.com/images/P/B00005JKQX.01.LZZZZZZZ.jpg

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Comparison Shopping

Lowest price of the DVD: “The Matrix”?

Applications

Comparison shopping

Supply-chain management

Supplier 2

… Integrator

Supplier M

Supplier 1

Buyer 2

Buyer M

Buyer 1

…

http://www.bizrate.com/marketplace/index.xpml

http://www.dealtime.com/

http://www.bizrate.com/marketplace/index.xpml

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Mediation architecture

Mediator

Wrapper

Source 1

Wrapper

Source 2

Wrapper

Source n

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• Sources are heterogeneous:– Different data models: relational, object-oriented, XML, …– Different schemas and representations. E.g.,

“Keanu Reeves” or “Reeves, Keanu” or “Reeves, K.” etc.• Describe source contents• Use source data to answer queries• Sources have limited query capabilities• Data quality• Performance• … …

Challenges

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Research projects

• Garlic (IBM),• Information Manifold (AT&T)• InfoSleuth (MCC),• Tsimmis, InfoMaster (Stanford)• Internet Softbot/Razor/Tukwila (U Wash.)• Hermes (Maryland)• Telegraph / Eddies (UC Berkeley)• Niagara (Univ Wisconsin)• DISCO, Agora (INRIA, France)• SIMS/Ariadne (USC/ISI)• Emerac/Havasu (ASU)

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Industry

• Nimble Technology• Enosys Markets• IBM• BEA

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Virtual integration

• Leave the data in the sources• When a query comes in:

– Determine the relevant sources to the query– Break down the query into sub-queries for the sources– Get the answers from the sources, filter them if needed and combine

them appropriately• Data is fresh• Otherwise known as

On Demand Integration

Slides from Dr. Michalis Petropoulos

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Mediator

Virtual Integration Architecture

DataSource

DataSource

GlobalSchema

LocalSchema

LocalSchema

Query Result

Wrapper Wrapper

End User

Design-Time

MediationLanguage

Mapping Tool

Run-Time

QueryReformulation

Optimization& Execution

XML

Web Services

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Design-Time

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Mediator


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Mediator


DataSource

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Mediator


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Outline

• Basics: theories of conjunctive queries• Global-as-view (GAV) approach to data integration• Local-as-view (LAV) approach to data integration

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Conjunctive Queries (CQ’s) in Datalog

• Most common form of query; equivalent to select-project-join (SPJ) queries• Useful for data integration• Form: q(X) :- p1(X1), p2(X2),…, pn(Xn).• Head q(X) represents the query answers• Body p1(X1), p2(X2),…, pn(Xn) represents the query conditions

– The head is true if all the subgoals are true.– Each pi(Xi) is called a subgoal. Xi is a vector of variables or constants.– Shared variables represent join conditions– Constants represent “Attribute=const” selection conditions– A relation can appear in multiple predicates (subgoals)

head

body

subgoals

q(X) :- p1(X1), p2(X2), …, pn(Xn)

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Conjunctive queries

• Head and subgoals are atoms.• An atom consists of a predicate applied to zero or more

arguments• Predicates represent relations.• An atom is true for given values of its variables iff the

arguments form a tuple of the relation.• Whenever an assignment of values to all variables makes all

subgoals true, the rule asserts that the resulting head is also true.

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Conjunctive Queries: example

• Schemastudent(name, courseNum), course(number, Instructor)

• SQL SELECT name FROM student, course WHERE student.courseNum=course.number AND instructor=‘Li’;• Equal to:

ans(SN) :- student(SN, CN), course(CN,’Li’).

– Predicates student and course correspond to relations names– Two subgoals: student(SN, CN) and course(CN,’Li’)– Variables: SN, CN. Constant: ‘Li’– Shared variable, CN, corresponds to “student.courseNum=course.number”– Variable SN in the head: the answer to the query

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Why not SQL

• Datalog is more concise• Let us state some general principles

– e.g., containment of rules that are almost impossible to state correctly in SQL.

– Will see that later• Recursion is much easier to express in Datalog.

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Answer to a CQ

• For a CQ Q on database D, the answer Q(D) is a set of heads of Q if we:– Substitute constants for variables in the body of Q in all possible ways– Require all subgoals to be true

• Example: ans(SN) :- student(SN, CN), course(CN,’Li’).– Tuples are also called facts:

student(Jack, 184), student(Tom,215), …, course(184,Li), course(215,Li), …– Answer “Jack”: SNJack,CN184– Answer “Tom”: SNTom,CN215– Answer “Jack”: SNJack,CN215 (duplicate eliminated)

Number Instructor 184 Li 215 Li 214 Mehrotra 252 Gupta

Student Course

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Query containment

• For two queries Q1 and Q2, we say Q1 is contained in Q2, denoted Q1Q2, if any database D, we have Q1(D) Q2(D).

• We say Q1 and Q2 are equivalent, denoted Q1Q2, if Q1(D) Q2(D) and Q2(D) Q1(D).

• Example: Q1: ans(SN) :- student(SN, CN), course(CN, ’Li’).

Q2: ans(SN) :- student(SN, CN), course(CN, INS).

We have: Q1(D) Q2(D).

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Another example

Q1: p(X,Y) :- r(X,W), b(W,Z), r(Z,Y).

Q2: p(X,Y) :- r(X,W), b(W,W), r(W,Y).

• We have: Q2 Q1

• Proof:– For any DB D, suppose p(x,y) is in Q2(D). Then there is a w such that

r(x,w), b(w,w), and r(w,y) are in D.– For Q1, consider the substitution: X x, W w, Z w, Y y.

– Thus the head of Q1 becomes p(x,y), meaning that p(x,y) is also in Q1(D).

• In general, how to test containment of CQ’s?– Containment mappings

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Test containment

• Two approaches:1. Containment mappings.2. Canonical databases.

• Really the same in the simple CQ case covered so far.• Containment test is NP-complete, but CQ’s tend to be small so

here is one case where intractability doesn’t hurt you.

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Containment mappings• A containment mapping from Q2 to Q1: Map variables of Q2 to

variables of Q1, such that:– Head of Q2 becomes head of Q1;– Each subgoal of Q2 becomes some subgoal of Q1.

• It is not necessary that every subgoal of Q1 is the target of some subgoal of Q2.

• Q1 Q2 iff there is a containment mapping from Q2 to Q1. – Note that the containment mapping is opposite the containment --- it goes

from the larger (containing CQ) to the smaller (contained CQ).• Example:

Q1: p(X,Y) :- r(X,W), b(W,Z), r(Z,Y).

Q2: p(X,Y) :- r(X,W), b(W,W), r(W,Y).– Containment mapping from Q1 to Q2: X X, Y Y, W W, Z W– No containment mapping from Q2 to Q1:

• For b(W,W) in Q2, its only possible target in Q1 is b(W,Z)• However, we cannot have a mapping WW and WZ, since each variable cannot

be mapped to two different variables

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A slightly different example

Q1: p(X,Y):- r(X,Z), g(Z,Z), r(Z,Y).

Q2: p(A,B):- r(A,C), g(C,D), r(D,B).

Containment mapping m:m(A)=X;m(B)=Y;m(C)=m(D)=Z.

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Q1: p(X,Y):- r(X,Y), g(Y,Z).Q2: p(A,B):- r(A,B), r(A,C).

Q1 looks for:

Q2 looks for:

Another Example

X ZY

A B

C

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Q1: p(X,Y):- r(X,Y), g(Y,Z).

Q2: p(A,B):- r(A,B), r(A,C).

Containment mapping:m(A)=X;m(B)=m(C)=Y.

Example - Continued

Notice twosubgoals canmap to one.

And notevery subgoalneed be atarget.

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Example - Concluded

Q1: p(X,Y):- r(X,Y), g(Y,Z).Q2: p(A,B):- r(A,B), r(A,C).

• No containment mapping from Q1 to Q2.– g(Y,Z) cannot map anywhere, since there is no g subgoal in Q2.

• Thus, Q1 properly contained in Q2.

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Extending CQ’s• CQ’s with built-in predicates:

– We can add more conditions to variables in a CQ.– Example:

student(name, GPA, courseNum), course(number,instructor,year)Q1(SN) :- student(SN, G, CN), course(CN, ’Li’), G>=3.5.Q2(SN) :- student(SN, G, CN), course(CN, ’Li’), G>=3.5, Y < 2002.Q2(SN) Q1(SN).

• Datalog queries: – a (possibly infinite) set of CQ’s with (possibly) recursion– Example: parent(Parent, Child)– Query: finding all ancestors of Tom

ancestor(P,C) :- parent(P, C). ancestor(P,C) :- ancestor(P,X), parent(X, C).

result(P) :- ancestor(P, ‘tom’).

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• Although CQ theory first appeared at a database conference, the AI community has taken CQ’s to heart.

• CQ’s, or similar logics like description logic, are used in a number of AI applications.– Again, their design theory is really containment and equivalence.

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Outline

• Basics: theories of conjunctive queries• Global-as-view (GAV) approach to data

integration• Local-as-view (LAV) approach to data integration

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GAV approach to data integration

• Readings:– Jeffrey Ullman, Information Integration Using Logical Views, ICDT

1997. – Ramana Yerneni, Chen Li, Hector Garcia-Molina, and Jeffrey

Ullman, Computing Capabilities of Mediators, SIGMOD 1999.

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Global-as-view Approach

Mediator

• Mediator exports views defined on source relationsmed(Dealer,City,Make,Year) = R1 R2

• A query is posted on mediator views:SELECT * FROM medWHERE Year = ‘2001’;

ans(D,C,M, ‘2001’) :- med(D,C,M,‘2001’).• Mediator expands query to source queries:

SELECT * FROM R1, R2 WHERE Year = ‘2001’;

ans(D,C,M,’2001’) :- R1(D,C), R2(D,M, ‘2001’).

R1(Dealer,City) R2(Dealer, Make, Year)

med(Dealer,City,Make,Year) = R1 R2

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• Project: TSIMMIS at Stanford• Advantages:

– User queries are easy to define– Query transformation generation is straightforward

• Disadvantages:– Not all source information is exported:

– Not easily scalable: every time a new source is added, mediator views need to be changed.

• Research issues– Efficient query execution?– Deal with limited source capabilities?

GAV Approach

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Limited source capabilities

Complete scans of relations not possible

Reasons:– Legacy databases or structured files: limited interfaces

– Security/Privacy

– Performance concerns

Example 1: legacy databases with restrictive interfaces

Ullman DBMS

Knuth TeX

… …

author titleGiven an author, return the books.

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Another example: Web search forms

www.imdb.com

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Problems

• How to describe source restrictions?• How to compute mediator restrictions from sources? • How to answer queries efficiently given these restrictions?• How to compute as many answers as possible to a query?• …

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Computing mediator restrictions

• Motivation: do not want users to be frustrated by submitting a query that cannot be answerable by the mediator

• Example:– Source 1: book(author?, title, price)

• Capability: “bff”• i.e., we must provide an author, and can get title and price info

– Source 2: review(title?, reviewer, rate)• Capability: “bff”• i.e., we must provide a book title, and can get other info

– Mediator view: MedView(A?,T,P,RV,RT) :- book(A,T,P),review(T,RV,RT).

– Query on the mediator view:• Ans(RT) :- MedView(A, ‘db’, P, RV, RT).• I.e., “find the review rates of DB books”

– But the mediator cannot answer this query, since we do not know the authors.• We want to tell the user beforehand what queries can be answered

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Outline

• Basics: theories of conjunctive queries;• Global-as-view (GAV) approach to data integration;• Local-as-view (LAV) approach to data integration.

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Local-as-view (LAV) approach

Mediator

• There are global predicates, e.g., “car,” “person,” “book,” etc.• They can been seen as mediator views• The content of each source is described using these global predicates• A query to the mediator is also defined on the global predicates• The mediator finds a way to answer the query using the source

contents

sources

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Example

Mediator

• Global predicates: Loc(Dealer,City),Sell(Dealer,Make,Year)• Source content defined on global predicates:

S1(Dealer,City) :- Loc(Dealer, City).S2(Dealer,Make,Year) :- Sell(Dealer, Make, Year).

In general, each definition could be more complicated, rather than direct copies.• Queries defined on global predicates.

Q: ans(D,M,Y) :- Loc(D, ’windsor’), Sell(D, M, Y).– Users do not know source views.

• The mediator decides how to use source views to answer queries.– “Answering queries using views”:

ans(D, M, Y) :- S1(D,’windsor’), S2(D,M,Y).

S1(Dealer,City) S2(Dealer,Make,Year)

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Answering queries using views

Mediator

• Source views can be complicated: SPJs, arithmetic comparisons,…• Not easy to decide how to answer a query using source views

Query: ans(D,M) :- Loc(D,‘windsor'), Sell(D,M,Y).

Rewriting: ans(D,M) :- V3(D,‘windsor’, M,Y). ans(D,M) :- V1(D,’windsor’), V2(D,M,Y).

…– “Equivalent rewriting”: compute the “same” answer as the query– A rewriting can join multiple source views

V1(Dealer,City):- Loc(Dealer, City).V2(Dealer,Make,Year):-Sell(Dealer, Make, Year).V3(D,C,M,Y) :- Loc(D,C),Sell(D,M,Y).V4(D,C,M,Y) :- Loc(D,C),Sell(D,M,Y), Y<1970.

Query

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Arithmetic comparisons

Mediator

• Comparisons can make the problem even trickier• Query: ans(D,M) :- Loc(D,‘windsor'), Sell(D,M,Y).

Rewriting: ans(D,M) :- V(D,‘windsor’, M,Y).

Contained rewriting: only retrieve cars before 1970. • Query: ans(D,M):- Loc(D, ‘windsor'), Sell(D,M,Y), Y < 1960.

Rewriting: ans(D,M) :- V(D,‘windsor’, M, Y), Y < 1960.

V(D,C,M,Y):- Loc(D,C),Sell(D,M,Y),Y<1970.

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Local-as-View (LAV)

Source1

Source2

Source3

Source4

Source5

Local Schema LocalSchema

LocalSchema

LocalSchema

Global Schema

BookISBNTitleGenreYear

AuthorISBNName

R1ISBNTitleName

Local Schema

R5ISBNTitle

Books before 1970 Humor Books

Create View R1 ASSELECT B.ISBN, B.Title, A.NameFROM Book B, Author AWHERE A.ISBN = B.ISBN AND B.Year < 1970

R1(ISBN, Title, Name):-Book(ISBN, Title, Genre,Year), Author(ISBN, Name), Year<1970.

Create View R5 ASSELECT B.ISBN, B.TitleFROM Book BWHERE B.Genre = ‘Humor’

R5(ISBN, Title):-Book(ISBN, Title, ‘humor’, Year).

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LAV details

• Query: Find authors of humor books Q(Name):-Book(ISBN,Title,”humor”,YEAR), Author(ISBN, Name)

• Views:R1(ISBN, Title, Name):- Book(ISBN, Title, Genre,Year), Author(ISBN, Name), Year<1970.R5(ISBN, Title) :-Book(ISBN, Title, ‘humor’, Year).

• Rewriting of Q using views:Q’(Name):-R1(ISBN, Title, Name), R2(ISBN, Title)

• Expansion of Q’Q’’(Name):- Book(ISBN, Title, Genre,Year), Author(ISBN, Name), Year<1970, Book(ISBN, Title, ‘humor’, Year).

Q’’’(Name):- Author(ISBN, Name), Year<1970, Book(ISBN, Title, ‘humor’, Year).

• Q’’’ is contained in Q

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Query Rewritings

• Given a query Q and a set of views V:– A conjunctive query P is called a “rewriting” of Q using

V if P only uses views in V, and P computes a partial answer of Q. That is: Pexp Q. A rewriting is also called a “contained rewriting” (CR).

– A conjunctive query P is called an “equivalent rewriting” (ER) of Q using V if P only uses views in V, and P computes the exact answer of Q. That is: Pexp Q.

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Bucket algorithm

• It is the basic method for query rewriting

• Each subgoal 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

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The Bucket Algorithm: Example

V1(Std,Crs,Qtr,Title) :- reg(Std,Crs,Qtr), course(Crs,Title), Crs ≥ 500, Qtr ≥ Aut98V2(Std,Prof,Crs,Qtr) :- reg(Std,Crs,Qtr), teaches(Prof,Crs,Qtr)V3(Std,Crs) :- reg(Std,Crs,Qtr), Qtr ≤ Aut94V4(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

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PProf, CCrs, QQtr

Note: Arithmetic predicates don’t pose a problem in this step

V2

Buckets

V4

teaches reg course

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SStd, CCrs, QQtr

Note: V3 doesn’t work: arithmetic predicates not consistentV4 doesn’t work: S not in the output of V4

V2

Buckets

V4

teaches reg course

V1V2

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CCrs, TTitle V2

Buckets

V4

teaches reg course

V1V2

V1V4

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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?)

V2V4

teaches reg course

V1V2

V1V4

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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 r’s 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 TT’

Minimized unfolding of rewriting 1:q1m’(S,C,P) :- t(P,C,Q), r(S,C,Q), c(C,T’), C ≥ 500, Q ≥ Aut98Minimized rewriting 1:q1m(S,C,P) :- V2(S’,P,C,Q), V1(S,C,Q,T’)

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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’)

V2V4

teaches reg course

V1V2

V1V4

V2V4

teaches reg course

V1V2

V1V4

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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

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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?

V4

Buckets

V6

cites cites sameTopic

V4

V6

V5

V6

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Bucket algorithm• Query:

q(x):-car(x), sell(x, d), loc(d, ’windsor’).• Views:

v1(x) :- car(x).v2(x) :- car(x), sell(x, d).v3(x,d) :- sell(x, d), loc(d, ’windsor’).v4(x) :- sell(x, d), loc(d, ’windsor’).

Car(x) Sell(x,d) Loc(d,’windsor’)

V1(x)

V2(x) v2(x)

V3(x,d) V3(x,d)

V4(x) V4(x)

q(x):-v1(x), v2(x), v3(x,d).

q(x):-v1(x), v3(x,d).

q(x):-v1(x), v4(x).

q(x):-v2(x), v3(x,d).

q(x):-v2(x), v4(x).

…

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• Projects: Information Manifold, Infomaster, Tukwila, …• Advantages:

– Scalable: new sources easy to add without modifying the mediator views

– All we need to do is to define the new source using the existing mediator views (predicates)

• Disadvantages:– Hard to decide how to answer a query using views

• Reading: Alon Halevy, Answering Queries Using Views: A Survey.

Projects using the LAV approach

1 Data integration Most slides are borrowed from Dr. Chen Li, UC Irvine.

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