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Searching and Integrating Information on the Web. Seminar 2: Data Integration Professor Chen Li UC Irvine. Motivation. Biblio sever. Legacy database. Plain text files. Support seamless access to autonomous and heterogeneous information sources. Comparison Shopping. Applications.

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Searching and integrating information on the web

Searching and Integrating Information on the Web

Seminar 2: Data Integration

Professor Chen Li

UC Irvine


Biblio sever

Legacy database

Plain text files

Support seamless access to autonomous and heterogeneous information sources.

Seminar 2


Comparison Shopping


  • Comparison shopping

Lowest price of the

DVD: “The Matrix”?

  • Supply-chain management

Buyer 1

Supplier 1

Buyer 2

Supplier 2


Supplier M

Buyer M

Seminar 2

Mediation architecture
Mediation architecture





Source 1

Source 2

Source n

TSIMMIS (Stanford), Garlic (IBM), Infomaster (Stanford), Disco (INRIA), Information Manifold (AT&T), Hermes(UMD), Tukwila (UW), InfoSleuth (MCC), …

Seminar 2


  • 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

Seminar 2


  • Basics: theories of conjunctive queries

  • Global-as-view (GAV) approach to data integration

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

Seminar 2

Basics conjunctive queries
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

Seminar 2

Conjunctive queries cq s
Conjunctive Queries (CQ’s)

  • 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 “Attribute=const” selection conditions

    • A relation can appear in multiple predicates (subgoals)

Seminar 2

Conjunctive queries example
Conjunctive Queries: example

  • student(name,courseNum), course(number,instructor)

    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

Seminar 2

Answer to a cq
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)



Seminar 2

Query containment
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).

Seminar 2

Another example
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

    • Canonical databases

Seminar 2

Containment mappings
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

Seminar 2

Example of containment mappings
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.

Seminar 2

Theorem of containment mappings
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 Q1’s 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

Seminar 2

Proof only if
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: Xreplaced 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)}

Seminar 2

Proof only if cont
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

Seminar 2

Testing query containment
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 CQ’s is NP-complete.

  • Some polynomial-time algorithms exist in special cases.

Seminar 2

Extending cq s
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)

      ans(SN) :- student(SN, G, CN), course(CN,’Li’), G>=3.5

      ans(SN) :- student(SN, G, CN), course(CN,’Li’, Y), G>=3.5, Y < 2002

    • More results on CQ’s with built-in predicates

  • Datalog queries:

    • a (possibly infinite) set of CQ’s 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’)

Seminar 2

Further reading
Further Reading

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

Seminar 2


  • Basics: theories of conjunctive queries

  • Global-as-view (GAV) approach to data integration

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

Seminar 2

Gav approach to data integration
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.

Seminar 2

Global as view approach
Global-as-view Approach

med(Dealer,City,Make,Year) = R S



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)

Seminar 2

Gav approach cont
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?

Seminar 2

Limited source capabilities
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



Given an author,

return the books.





Seminar 2

Another example web search forms
Another example: Web search forms

Seminar 2


  • 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?

Seminar 2

Describe source capabilities: using attribute adornments.

f: free

b: bound

u: unspecified

c[S]: chosen from a list S of constants, e.g., “state”

o[S]: 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




Seminar 2

Computing mediator restrictions
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

Seminar 2

Solutions compute mediator capabilities
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

Seminar 2

Union views
“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, o[s3]  o[s3]”

    • “c[s2], o[s3]  c[s2s3]”

    • Invalid combination: “b,u  -”



Seminar 2

Union views with postprocessing
“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, o[s3]  f” instead of “o[s3]”

    • “c[s2], o[s3]  c[s2]” instead of “c[s2s3]”

    • “b,u  b” instead of “invalid combination”



Seminar 2

Join views with passing bindings
“Join” views with passing bindings

  • Assumption:

    • MedView :- V1 JOIN V2

    • The mediator can pass bindings from V1 to V2

    • So the join order matters



Seminar 2

Other views
Other views

  • Union

  • Join

  • Selection

  • Projection

  • Multiple views

Seminar 2

Concise template description
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




Adornment n1 is at least as restrictive as adornment n2





Adornment n1 is at least as restrictive as adornment n2,

if the constant set of n1 is a subset of that of n2



Adornment graph

Seminar 2


  • Basics: theories of conjunctive queries

  • Global-as-view (GAV) approach to data integration

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

Seminar 2

Local as view lav approach
Local-as-view (LAV) approach



  • 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

Seminar 2





  • Global predicates: Loc(Dealer,City),Sell(Dealer,Make,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)

Seminar 2

Another lav example
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’)

Seminar 2

Open world assumption owa and close world assumption cwa





All car tuples

W1 = W2 =

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.

Seminar 2

Projects using the lav approach
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

Seminar 2


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

Seminar 2

Answering queries using views
Answering queries using views



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

Seminar 2

Arithmetic comparisons
Arithmetic comparisons


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

  • 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 < 1960

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

Seminar 2

Dropping attributes in views
Dropping attributes in views


Drop “Year” in the view:

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

  • A variable in a CQ is called:

    • “distinguished”: if it appears in the query’s head

    • “nondistinguished”: otherwise

  • The problem becomes even harder when we have nondistinguished variables.

  • Query: ans(D,M) :- Loc(D,'irvine'), Sell(D,M,Y), Y<1960

    No rewriting! Since we do not have “Year” information.

  • Query: ans(D,M) :- Loc(D,'irvine'), Sell(D,M,Y), Y<1980

    Contained rewriting: ans(D,M) :- V(D, ‘irvine’, M)

Seminar 2



Source views

  • How to answer a query using views?

  • We will focus on the case where both the query and views are simply conjunctive.

Seminar 2

Query expansion
Query Expansion

  • For each query P on views, we can expandP 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()

Seminar 2


  • 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.”

Seminar 2

Focus minicon algorithm
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

Seminar 2


  • 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’)

Seminar 2

Mcds enhanced buckets
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)

Seminar 2

Multi subgoal mcd
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.

Seminar 2

General rules
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, it’s impossible for W to join with other views to answer conditions involving X.

      • I.e., “either NONE or ALL.”

Seminar 2

Combine mcds to cover query subgoals
Combine MCDs to cover query subgoals

  • Problem:

    • q(x) :- car(x), sell(x,d), loc (d,“la")

    • 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")

  • MCDs:

    • car(x) : v1(x), v2(x)

    • sell(x,d) : v3(x,d)

    • loc(d,"ca") : v3(x,d)

    • sell(x,d),loc(d,“la") : v4(x)

  • Contained rewritings - using MCDs to cover all query subgoals, without overlap

    • P1: q(x) :- v1(x), v3(x,d), v3(x,d)

    • P2: q(x) :- v2(x), v3(x,d), v3(x,d)

    • P3: q(x) :- v1(x), v4(x)

    • P4: q(x) :- v2(x), v4(x)

  • MCR: union of these four contained rewritings.

Seminar 2

Related references
Related references


Source views

  • Other algorithms on AQUV:

    • Bucket, Inverse-rule

  • Generating efficient equivalent rewritings of queries using views:

    • CoreCover algorithm: [Afrati, Li, Ullman, SIGMOD’01]

  • Handling arithmetic comparisons and dropped attributes:

    • [Afrati, Li, Mitra, PODS’02]

    • [Afrati, Li, Mitra, EDBT’04]

Seminar 2