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Query Planning with Limited Source Capabilities

Chen Li Stanford University

Edward Y. ChangUniversity of California, Santa Barbara

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• Heterogeneous information sources on the WWW

• Information-integration systems

• Limited query capabilities

– Music stores: amazon.com, cdnow.com.– Must specify a value of Artist or Title.

– The sources do not answer queries such as “Give me all your information about CDs.”

Motivation

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Sources View Schemas Must Bind

1 v1(Song, CD) Song2 v2(CD, Artist, Price) CD3 v3(CD, Artist, Price) Artist

Query: “Find the prices of CDs containing a song titled Friends.”

Example

v1(Friends, CD) v2(CD, Artist, Price)v1(Friends, CD) v3(CD, Artist, Price)

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Source tuples

v1(Song, CD)

<Friends, Love>

<Friends, Life>

v2(CD, Artist, Price)

<Love, Lucy, $15><Story, Snoopy, $14>

v3(CD, Artist, Price)

<Story, Lucy, $13>

<Love, Snoopy, $10>

<Life, Charlie, $8>

Not all the tuples couldbe retrieved from thesources due to the restrictions.

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Traditional approach: consider each join at a time.

v1 v2: {$15}

v1 v3: empty, no binding for Artist.

v1(Song, CD)

<Friends, Love>

<Friends, Life>

v2(CD, Artist, Price)

<Love, Lucy, $15><Story, Snoopy, $14>

v3(CD, Artist, Price)

<Story, Lucy, $13>

<Love, Snoopy, $10>

<Life, Charlie, $8>

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Our approach: retrieve as many tuples as possible.

X

X

X

X

X

XThis approach could savethe user $15 - $10 = $5!

v1(Song, CD)

<Friends, Love>

<Friends, Life>

v2(CD, Artist, Price)

<Love, Lucy, $15><Story, Snoopy, $14>

v3(CD, Artist, Price)

<Story, Lucy, $13>

<Love, Snoopy, $10>

<Life, Charlie, $8>

v1 v2: {$15}v1 v3: {$10}

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• Access views not in a join to retrieve bindings;• Recursive process;• Some tuples in the answer cannot be retrieved.

X

X

X

X

X

X

v1(Song, CD)

<Friends, Love>

<Friends, Life>

v2(CD, Artist, Price)

<Love, Lucy, $15><Happy, Snoopy, $14>

v3(CD, Artist, Price)

<Happy, Lucy, $13>

<Love, Snoopy,$10>

<Life, Charlie, $8>

Observations

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• How to compute the maximal answer?• When should we access sources not in a query?• What sources should be accessed?

Questions

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Source views

• A set of source views V with binding patterns:– b: a value must be specified for the attribute– f: free

• Each view schema uses a set of global attributes

CD Artist PriceSong

b fv1(Song, CD)

b f fv2(CD, Artist, Price)

f b fv3(CD, Artist, Price)

Hypergraph representation:

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A query Q includes:– Input attributes: I;

– Output attributes: O.

Queries

Input attribute: {Song}Output attribute: {Price}

CD Artist PriceSong

v1(Song, CD)

v2(CD, Artist, Price)

v3(CD, Artist, Price)

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• Connection: a set of views that connect I and O in Q.

• Meaning: natural join of the views.

• Universal-relation-like assumptions, but connections can be generated in various ways.

Connections

T1={v1,v2}, T2={v1,v3}

CD Artist PriceSong

v1(Song, CD)

v2(CD, Artist, Price)

v3(CD, Artist, Price)

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Question 1: Computing the maximal answer

• Translate a query and source views into a Datalog program.

• Borrowed the idea from Duschka and Levy [IJCAI-97]. – We eliminate useless source accesses.

• Why Datalog programs? Recursion.

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Constructing program (Q,V)Connection rules: ans(P) :- V1(s1, C) & V2 (C, A, P) ans(P) :- V1(s1, C) & V3 (C, A, P)Fact rule: song(s1) :-

}v1(Song, CD)-rule: V1(S, C) :- song(S) & v1(S,C)Domain rule: cd(C) :- song(S) & v1(S, C)

}v2(CD, Artist, Price)

}v3(CD, Artist , Price)

V2(C, A, P) :- cd(C) & v2(C, A, P)artist(A) :- cd(C) & v2(C, A, P)price(P) :- cd(C) & v2(C, A, P)V3(C, A, P) :- artist(A) & v3(C, A, P)cd(C) :- artist(A) & v3(C, A, P)price(P) :- artist(A) & v3(C, A, P)

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• Binding assumptions:

– A binding for an attribute is from the attribute’s domain;

– Do not allow the “strategy” of trying all the possible strings to “test” the source (may not terminate);

– Any binding is either obtained from the query, or from a tuple returned by a source query.

• The program (Q,V) computes the maximal answer.

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A

B

C D

E F

f f bv2(A, B, C)

b fv3(C, D)

b fv1(A, C)

b fv5(E, F)

f fv4(C, E)

Query: Input: A = a1

Output: D = ?Connections: T1 = {v1,v3}, T2 = {v2,v3}

Not all the views need to accessed.

Question 2: when to access off-query sources?

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• T1: accessing outside T1 sources is NOT necessary.

A C v3(C, D)v1(A, C) D

• T2: accessing outside T2 sources is necessary to get

C bindings.

AB

C D

v2(A, B, C)

v3(C, D)

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Independent connections• A connection T is independent if all the views in T can be

queried starting from the input attributes as the initial bindings and using only the views in T.

• T2 is not independent, it needs C bindings.

AB

C D

v2(A, B, C)

v3(C, D)

• T1 is independent. A C v3(C, D)v1(A, C) D

• Theorem: off-connection source accesses are only necessary for nonindependent connections.

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• A view v is relevant to connection T if we may miss some answers to T when v is not used.

A

B

C D

E F

v2(A, B, C)

v3(C, D)v1(A, C)

v5(E, F)v4(C, E)

• The relevant views of T2 are: v2, v3 , v1, v4 .

• How to find all the relevant views of a nonindependent connection?

Question 3: what sources should be accessed?

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Kernel• A kernel of a connection is a minimal set of attributes that

need to be initially bound in addition to the input attributes to query the full connection.

• A connection may have multiple kernels.

• T1 has one kernel: {} A C v3(C, D)v1(A, C) D

• T2 has one kernel: {C}

AB

C D

v2(A, B, C)

v3(C, D)

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Algorithm FIND_REL: Finding relevant views of a connection

Find all the relevant views of connection T2 = {v2,v3}:

A

B

C D

E F

v2(A, B, C)

v3(C, D)v1(A, C)

v5(E, F)v4(C, E)

(1) Compute queryable views: {v1,v2 ,v3,v4,v5};(2) Find a kernel K of T2 : K = {C};

(4) Return R T2 = {v1,v2 ,v3 ,v4}.

(3) Compute all the views that can help produce bindings for the attributes in K: R = {v1,v2 ,v4} ;

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Constructing an efficient program

• Compute the relevant views for each connection; • Take the union of all these relevant source views;• Use these views to construct a new program;• Remove useless rules.

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Conclusions

• A query-planning framework to compute the maximal answer to a query (Duschka and Levy [IJCAI-97]).

• Techniques for telling when to access off-query views;

• Algorithms:– finding all the relevant sources for a query;

– constructing an efficient program.

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Other related work

• Rajaraman, Sagiv, and Ullman [PODS-95]: – Shows how to find an equivalent query rewriting using views with

binding restrictions;

– We give the maximal rewriting of a query.

• Optimizing conjunctive queries with binding restrictions:– Yerneni, Li, Garcia-Molina, and Ullman [ICDT-99];

– Florescu et al. [SIGMOD-99].

• Testing connection containment:– Li [Stanford-CS-TR 2000], using results of monadic programs to

prove the problem is decidable.

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Predicates

EDB predicates IDB predicatesv1(S, C) V1 (S, C)v2(C, A,P) V2 (C, A, P)v3(C, A, P) V3 (C, A, P)

cd(C)song(S)artist(A)price(P)

ans(P)

}-predicates

}domain predicates

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Evaluating program (Q,V)

• Assume the right side of an -rule or a domain rule is:

domA1(A1), …, domAp(Ap), vi(A1,…, Am)

• Once we have bindings for domA1(A1), …, domAp(Ap), evaluate the rule and populate the domain predicates and -predicate.

• Repeat until no more facts can be derived.• Compute the maximal answer to the query.

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Forward-closureGiven views W V, and attributes X, the forward-closure of X given W, denoted f-closure(X,W), is the the set of views in W that can be eventually queried by using the views in W, starting from the initial bindings X.

f-closure({A},{v1,v2,v3}) = {v1,v2,v3}

f-closure({D},{v1,v2,v3}) = {}

A

B

C D

E F

v2(A, B, C)

v3(C, D)v1(A, C)

v5(E, F)v4(C, E)

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• Backward-closure of a set of attributes X: b-closure(X), is the set of views that can help retrieve bindings for X.

Backward-closure

• Lemma: All backward-closures of a connection are the same.

b-closure(C) = {v1,v2,v4}

A

B

C D

E F

v2(A, B, C)

v3(C, D)v1(A, C)

v5(E, F)v4(C, E)

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• BF-chain:

• Backward-closure:

BF-chain, backward-closure

free

bound bound bound

freefree

A

B

C D

E F

v2(A, B, C)

v3(C, D)v1(A, C)

v5(E, F)v4(C, E)

b-closure(C) = {v1,v2,v4}

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Other possibilities of obtaining bindings

• Cached data: For a cached tuple ti(a1,a2) for view vi(A1,A2), add the following rules to the program (Q, V):

vi(a1,a2) :-

domA1(a1) :-

domA2(a2) :-

• Domain knowledge: – student(name, dept, GPA).

– dept = CS, Physics, Chemistry, etc.

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Computing a partial answer

• Independent connections: complete answers are computable.

• Nonindependent connections: access some relevant views. May terminate evaluating the program after some results are computed.