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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.