Searching and Integrating Information on the Web

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Title: Searching and Integrating Information on the Web

1
Searching and Integrating Information on the Web

Seminar 2 Data Integration
Professor Chen Li
UC Irvine

2
Motivation
Biblio sever
Legacy database
Plain text files
Support seamless access to autonomous and
heterogeneous information sources.
3
Applications

Comparison shopping

Lowest price of the DVD The Matrix?

Supply-chain management

Buyer 1
Supplier 1
Buyer 2
Supplier 2
Integrator

Supplier M
Buyer M
4
Mediation architecture
Mediator
Wrapper
Wrapper
Wrapper
Source 1
Source 2
Source n
TSIMMIS (Stanford), Garlic (IBM), Infomaster
(Stanford), Disco (INRIA), Information Manifold
(ATT), Hermes(UMD), Tukwila (UW), InfoSleuth
(MCC),
5
Challenges

Sources are heterogeneous
Different data models relational,
object-oriented, XML,
Different schemas and representations
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

6
Outline

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

7
Basics conjunctive queries

Reading Ashok K. Chandra and Philip M. Merlin,
Optimal implementation of conjunctive queries in
relational data bases, STOC, 77-90, 1977.
Fundamental for data integration
Source content description
Query description
Plan formulation

8
Conjunctive Queries (CQs)

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
Each pi(Xi) is called a subgoal
Shared variables represent join conditions
Constants represent Attributeconst selection
conditions
A relation can appear in multiple predicates
(subgoals)

9
Conjunctive Queries example

student(name,courseNum), course(number,instructor)
SELECT name
FROM student, course
WHERE student.courseNumcourse.number
AND instructorLi
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.courseNumcourse.number
Variable SN in the head the answer to the query

10
Answer to a CQ

For a CQ Q on database D, the answer Q(D) is 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 EDB (external database)
facts student(Jack, 184), student(Tom,215), ,
course(184,Li), course(215,Li),
Answer Jack SN?Jack,CN?184
Answer Tom SN?Tom,CN?215
Answer Jack SN?Jack,CN?215 (duplicate
eliminated)

Course
Student
11
Query containment

For two queries Q1 and Q2, we say Q1 is contained
in Q2, denoted Q1?Q2, if any database D, we have
Q1(D) ?Q2(D).
We say Q1 and Q2 are equivalent, denoted Q1?Q2,
if Q1(D) ?Q2(D) and Q1(D) ? Q2(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).

12
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 CQs?
Containment mappings
Canonical databases

13
Containment mappings

Mapping from variables of CQ Q2 to variables of
CQ Q1, such that
Head of Q2 becomes head of Q1
Each subgoal of Q2 becomes some subgoal of Q2
It is not necessary that every subgoal of Q1 is
the target of some subgoal of Q2.
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 W?W and W?Z,
since each variable cannot be mapped to two
different variables

14
Example of containment mappings

Example C1 p(X) - a(X,Y), a(Y,Z), a(Z,W)
C2 p(X) - a(X,Y), a(Y,X)
Containment mapping from C1 to C2 X ? X, Y ? Y,
Z ? X, W ? Y
No containment mapping from C2 to C1. Proof
For the two heads, the mapping must have X ? X
For a(X,Y) in C2, its target in C1 can only be
a(X,Y) (since X?X). Thus Y?Y.
However, for a(Y,X) in C2, its target, which must
be a(Y,X), does not exist in C1.

15
Theorem of Containment Mappings

Theorem Q1 ?Q2 iff there is a containment
mapping from Q2 to Q1.
Notice the direction is the opposite
Proof (If)
Suppose ? is a containment mapping from Q2 to Q1
For any DB D, let tuple t is in Q1(D)
t is produced by a substitution ? on the
variables of Q1 that makes all Q1s subgoals
facts in D.
Therefore, ? ? ? is a substitution for variables
of Q2 that produces t
Thus each t in Q1(D) must be in Q2(D)

Q1 p(X) - G1, G2, Gk
?
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)
?
Q2 p(X) - H1, H2, Hj
16
Proof (only if)

Key idea frozen CQ
Use a unique constant to replace a variable
Frozen Q is a DB consisting of all the subgoals
of Q, with the chosen constants substituted for
variables
This DB is called a canonical database of the
query.
Example
Q1 p(X,Y) - r(X,W), b(W,Z), r(Z,Y)
Frozen Q1 X replaced by constant x0, W by
constant w0, Z by z0, Y by y0
Result DB with r(x0, w0), b(w0, z0), r(z0, y0)

17
Proof (only if) -- cont

Let Q1 ?Q2. Let D be the frozen Q1. Let ? be the
substitution from those constants to the
variables in Q1.
Since we chose a unique constant for each
variable, this substitution exists.
Since Q1 ?Q2 the frozen head of Q1 must be in
Q2(D). Thus there is a substitution ? from Q2 to
D.
We can show that ? ? ? is a containment mapping
from Q2 to Q1
The head of Q2 is mapped to the head of Q1.
Each subgoal in Q2 is mapped to a subgoal in Q2.

Q1 p(X) - G1, G2, Gk
?
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)
?
Q2 p(X) - H1, H2, Hj
18
Testing query containment

To test Q1 ?Q2.
Get a canonical DB D of Q1.
Compute Q2(D)
If Q2(D) contains the frozen head of Q1, then Q1
?Q2. otherwise not.
Testing containment between CQs is NP-complete.
Some polynomial-time algorithms exist in special
cases.

19
Extending CQs

CQs with built-in predicates
We can add more conditions to variables in a CQ.
Example
student(name, GPA, courseNum),
course(number,instructor,year)
ans(SN) - student(SN, G, CN), course(CN,Li),
Ggt3.5
ans(SN) - student(SN, G, CN), course(CN,Li,
Y), Ggt3.5, Y lt 2002
More results on CQs with built-in predicates
Datalog queries
a (possibly infinite) set of CQs with (possibly)
recursion
Example r(Parent, Child)
Query finding all ancestors of Tom
ancestor(P,C) - r(P, C)
ancestor(P,C) - ancestor(P,X), r(X, C)
result(P) - ancestor(P, tom)

20
Further Reading

Jeff Ullman, Principles of Database and
Knowledge Systems, Computer Science Press, 1988,
Volume 2.

21
Outline

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

22
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.

23
Global-as-view Approach
med(Dealer,City,Make,Year) R S
Mediator
R1(Dealer,City)
R2(Dealer, Make, Year)

Mediator exports views defined on source
relations
med(Dealer,City,Make,Year) R1 R2
A query is posted on mediator views
SELECT FROM med
WHERE Year 2001 ans(D,C,M) -
med(D,C,M,2001)
Mediator expands query to source queries
SELECT FROM R1, R2
WHERE Year 2001 ans(D,C,M,Y) - R1(D,C),
R2(D,M,2001)

24
GAV Approach (cont)

Project TSIMMIS at Stanford
Advantages
User queries easy to define
Plan generation is straightforward
Disadvantages
Not all source information is exported
What if users want to get dealers that may not
the city information?
Those dealers are not visible.
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?

25
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

title
author
Given an author, return the books.
Ullman
DBMS
Knuth
TeX

26
Another example Web search forms
www.imdb.com
27
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?

28
Describe source capabilities using attribute
adornments. f free b bound u
unspecified cS chosen from a list S of
constants, e.g., state oS optional if
chosen, must be from a list S of constants A
search form is represented as multiple
templates (Title, Author, ISBN, Format,
Subject) b f u u
u ? 1 f b u u
u ? 1 u u u o
o ? 2 u u b u
u ? 3
1
2
3
29
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 a title, and can get author
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

30
Solutions Compute mediator capabilities

Need algorithms that do the following
Given
Source relations with restrictions.
Mediator views defined on source relations
Union
Join
Selection
Projection
Main idea of the algorithms
compute restrictions on mediator views
minimize number of view templates

31
Union views

Assumption
MedView - V1?V2
We want to get all tuples from two sources that
satisfy a query condition
No mediator post-processing power
Table to compute view adornments
E.g., f, os3 ? os3
cs2, os3 ? cs2?s3
Invalid combination b,u ? -

V2
V1
32
Union views with postprocessing

Mediator can postprocess results from a source,
and check if the results satisfy certain
conditions
Thus some entries are more relaxing
Essentially o can be treated as f, and u
can be treated as f
E.g., f, os3 ? f instead of os3
cs2, os3 ? cs2 instead of cs2?s3
b,u ? b instead of invalid combination

V2
V1
33
Join views with passing bindings

Assumption
MedView - V1 JOIN V2
The mediator can pass bindings from V1 to V2
So the join order matters

V2
V1
34
Other views

Union
Join
Selection
Projection
Multiple views

35
Concise template description

Some adornments subsume other adornments
E.g. f subsumes b, since every query
supported by b is also supported by f
Adornment graph subsumption relationships
Use the graph to compress templates
experiments shrank 26 ? 8 templates

f
n1
n2
Adornment n1 is at least as restrictive as
adornment n2
b
o
n1
n2
Adornment n1 is at least as restrictive as
adornment n2, if the constant set of n1 is a
subset of that of n2
u
c
Adornment graph
36
Outline

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

37
Local-as-view (LAV) approach
Mediator
sources

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

38
Example
Mediator
S1(Dealer,City)
S2(Dealer,Make,Year)

Global predicates Loc(Dealer,City),Sell(Dealer,Ma
ke,Year)
Source content defined on global predicates
S1(Dealer,City) - Loc(Dealer,City)
S2(Dear,Make,Year) - Sell(Dear,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,irvine), 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,irvine), S2(D,M,Y)

39
Another LAV Example

Mediator predicates car(C), sell(Car, Dealer),
loc(dealer, city)
Views
v1(x) - car(x)
v2(x) - car(x), sell(x, d)
v3(x,d) - sell(x, d), loc(d, la)
v4(x) - sell(x, d), loc(d, la)
Query q(x) - car(x), sell(x, d), loc(d, la)

40
Open-world assumption (OWA) and Close-world
assumption (CWA)
W1(Make, Dealer) - car(Make, Dealer) W2(Make,
Dealer) - car(Make, Dealer)

W1 and W2 have some car tuples.
E.g. W1 and W2 are from two different web sites.

W1 and W2 have all car tuples.
E.g. W1 and W2 are computed from the same car
table in a database.

41
Projects using the LAV approach

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

42
Reading

Alon Halevy, Answering Queries Using Views A
Survey.

43
Answering queries using views
Mediator
Query
V(D,C,M,Y) - Loc(D,C),Sell(D,M,Y)

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,'irvine'),
Sell(D,M,Y).
Rewriting ans(D,M) - V(D,irvine, M,Y)
Equivalent rewriting compute the same answer
as the query
A rewriting can join multiple source views
This problem exists in many other applications
data warehousing
web caching
query optimizations

44
Arithmetic comparisons
Mediator
V(D,C,M,Y)- Loc(D,C),Sell(D,M,Y),Ylt1970

Comparisons can make the problem even trickier
Query ans(D,M) - Loc(D,'irvine'),
Sell(D,M,Y).
Rewriting ans(D,M) - V(D,irvine, M,Y)
Contained rewriting only retrieve cars before
1970.
Query ans(D,M) - Loc(D, 'irvine'), Sell(D,M,Y),
Y lt 1960
Rewriting ans(D,M) - V(D,irvine,M,Y), Y lt 1960

45
Dropping attributes in views
Mediator
Drop Year in the view V(D,C,M)-
Loc(D,C),Sell(D,M,Y),Ylt1970

A variable in a CQ is called
distinguished if it appears in the querys
head
nondistinguished otherwise
The problem becomes even harder when we have
nondistinguished variables.
Query ans(D,M) - Loc(D,'irvine'), Sell(D,M,Y),
Ylt1960
No rewriting! Since we do not have Year
information.
Query ans(D,M) - Loc(D,'irvine'), Sell(D,M,Y),
Ylt1980
Contained rewriting ans(D,M) - V(D, irvine,
M)

46
Problems
Query
Source views

How to answer a query using views?
We will focus on the case where both the query
and views are simply conjunctive.

47
Query Expansion

For each query P on views, we can expand P using
the view definitions, and get a new query,
denoted as Pexp, on the base tables.
Pexp can be considered to be the real meaning
of the query.
Example
View V(D,C,M) - Loc(D,C), Sell(D,M,Y)
A query P using V ans(D,M) - V(D,la,M)
Expansion ans(D,M) - Loc(D,la), Sell(D,M,Y)

Query P ans() - v1(), v2(), , vk()
Expansion Pexp ans()- p1,1(),,p1,i1(),,
pk,1(),,pk,ik()
48
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.
A query P is called a maximally-contained
rewriting of Q using V if P is a union of CRs of
Q using V, and for any CR P1of Q, the answer to P
contains the answer to query P1, that is, P1exp ?
Pexp.
See earlier slides for examples
Notice that all these definitions depend on the
language of the rewriting considered. Here we
consider conjunctive queries.

49
Focus MiniCon algorithm

MiniCon Algorithm Rachel Pottinger and Alon
Levy, A scalable algorithm for answering queries
using views, VLDB 2000.
See also The Shared-variable-bucket algorithm by
Prasenjit Mitra "An Algorithm for Answering
Queries Efficiently Using Views" in Proceedings
of the Australasian Database Conference, Jan
2001.
Formulation
Input a conjunctive query Q and a set V of
conjunctive views
Output an maximally-contained rewriting (MCR) of
Q using V
Main idea
For each query subgoal and for each view
Check if the view can be used to answer the
query subgoal, and if so, in what form
Some shared variables are treated carefully
Combine views to answer all query subgoals
Reduced to a set-cover problem

50
Example

Query q(x) - car(x), sell(x, d), loc(d, la)
Views
v1(x) - car(x)
v2(x) - car(x), sell(x, d)
v3(x,d) - sell(x, d), loc(d, la)
v4(x) - sell(x, d), loc(d, la)

51
MCDs (enhanced Buckets)

For query subgoal car(x), its MCD includes all
views that can answer this subgoal
v1(x), v2(x)
MCD of query subgoal sell(x,d)
v3(x,d) only
but not v2(x)! Because
Variable d is nondistinguished, i.e., it is not
exported.
Variable d is shared by another query subgoal,
loc(d,la). If we were to use v2(x) to answer
query subgoal sell(x,d), we cannot get the dealer
info to join with the other view to answer
loc(d,la).
MCD of query subgoal loc(d,la)
v3(x,d)

52
Multi-subgoal MCD

MCD of query subgoals sell(x,d),loc(d,la)
v4(x)
If v4(x) is used to answer query subgoal
sell(x,d), then the query subgoal loc(d,la)
must be answered using v4(x) as well.
The reason is that d is shared by two query
subgoals, and the corresponding variable in v4(x)
is not exported.

53
General rules

For a query subgoal G and a view subgoal H in
view W, the MiniCon algorithm considers a mapping
from G to H
In this mapping, a query variable X is mapped to
a view variable A
Four possible cases
Case 1 X is dist., A is dist.. OK.
A is exported, so can join with other views.
Case 2 X is nondist., A is dist.. OK.
Same as above
Case 3 X is dist., A is nondist.. NOT OK.
X needs to be in the answer, but A is not
exported.
Case 4 X is nondist., A is nondist..
Then all the query subgoals using X must be able
to be mapped to other subgoals in view W.
Reason since A is not exported in W, its
impossible for W to join with other views to
answer conditions involving X.
I.e., either NONE or ALL.