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Query Planning with Limited Source Capabilities

Query Planning with Limited Source Capabilities. Chen Li Stanford University Edward Y. Chang University of California, Santa Barbara. Motivation. Heterogeneous information sources on the WWW Information-integration systems Limited query capabilities Music stores: amazon.com, cdnow.com.

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Query Planning with Limited Source Capabilities

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  1. Query Planning with Limited Source Capabilities Chen Li Stanford University Edward Y. Chang University of California, Santa Barbara

  2. Motivation • 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.”

  3. Sources View Schemas Must Bind 1 v1(Song, CD) Song 2 v2(CD, Artist, Price) CD 3 v3(CD, Artist, Price) Artist v1(Friends, CD) v2(CD, Artist, Price) v1(Friends, CD) v3(CD, Artist, Price) Example Query: “Find the prices of CDs containing a song titled Friends.”

  4. v2(CD, Artist,Price) <Love, Lucy, $15> v1(Song, CD) <Story, Snoopy, $14> <Friends, Life> <Friends, Love> v3(CD, Artist,Price) <Story, Lucy, $13> <Love, Snoopy, $10> <Life, Charlie, $8> Source tuples Not all the tuples could be retrieved from the sources due to the restrictions.

  5. v2(CD, Artist,Price) v1 v2: {$15} <Love, Lucy, $15> v1(Song, CD) <Story, Snoopy, $14> <Friends, Life> <Friends, Love> v3(CD, Artist,Price) <Story, Lucy, $13> v1 v3: empty, no binding for Artist. <Love, Snoopy, $10> <Life, Charlie, $8> Traditional approach: consider each join at a time.

  6. v2(CD, Artist,Price) <Love, Lucy, $15> v1(Song, CD) <Story, Snoopy, $14> <Friends, Life> <Friends, Love> X v3(CD, Artist,Price) X v1 v2: {$15} <Story, Lucy, $13> v1 v3: {$10} <Love, Snoopy, $10> <Life, Charlie, $8> Our approach: retrieve as many tuples as possible. X X X X This approach could save the user $15 - $10 = $5!

  7. v2(CD, Artist,Price) <Love, Lucy, $15> v1(Song, CD) <Happy, Snoopy, $14> X <Friends, Life> X <Friends, Love> X v3(CD, Artist,Price) X <Happy, Lucy, $13> X <Love, Snoopy,$10> X <Life, Charlie, $8> Observations • Access views not in a join to retrieve bindings; • Recursive process; • Some tuples in the answer cannot be retrieved.

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

  9. Hypergraph representation: b f f v2(CD, Artist,Price) Song CD Artist Price f b f v3(CD, Artist,Price) b f v1(Song, CD) 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

  10. v2(CD, Artist,Price) Song CD Artist Price Input attribute: {Song} Output attribute: {Price} v3(CD, Artist,Price) v1(Song, CD) Queries A query Q includes: • Input attributes: I; • Output attributes: O.

  11. v2(CD, Artist,Price) Song CD Artist Price T1={v1,v2}, T2={v1,v3} v3(CD, Artist,Price) v1(Song, CD) Connections • 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.

  12. 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.

  13. } -rule: V1(S, C) :- song(S) & v1(S,C) Domain rule: cd(C) :- song(S) & v1(S, C) v1(Song, CD) } 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) v2(CD, Artist,Price) } v3(CD, Artist ,Price) 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) :-

  14. 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.

  15. f f b v2(A, B, C) b f v3(C, D) B A C D b f v1(A, C) f f v4(C,E) E F b f v5(E, F) Question 2: when to access off-query sources? Query: Input: A = a1 Output: D = ? Connections: T1 = {v1,v3}, T2 = {v2,v3} Not all the views need to accessed.

  16. T1: accessing outside T1 sources is NOT necessary. v1(A, C) v3(C, D) C A D • T2: accessing outside T2 sources is necessary to get • C bindings. v2(A, B, C) B v3(C, D) C A D

  17. v1(A, C) v3(C, D) C A D • T1 is independent. • T2 is not independent, it needs C bindings. v2(A, B, C) B v3(C, D) C A D 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. • Theorem: off-connection source accesses are only necessary for nonindependent connections.

  18. v2(A, B, C) B v1(A, C) v3(C, D) C A D • The relevant views of T2 are: v2, v3 , v1, v4 . v4(C,E) v5(E, F) E F Question 3: what sources should be accessed? • A view v is relevant to connection T if we may miss some answers to T when v is not used. • How to find all the relevant views of a nonindependent • connection?

  19. v1(A, C) v3(C, D) C A D • T1 has one kernel: {} • T2 has one kernel: {C} v2(A, B, C) B v3(C, D) C A D 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.

  20. v2(A, B, C) B v1(A, C) v3(C, D) C A D v4(C,E) v5(E, F) E F Algorithm FIND_REL: Finding relevant views of a connection Find all the relevant views of connection T2 = {v2,v3}: (1) Compute queryable views: {v1,v2 ,v3,v4,v5}; (2) Find a kernel K of T2 : K = {C}; (3) Compute all the views that can help produce bindings for the attributes in K: R = {v1,v2 ,v4} ; (4) Return R  T2 = {v1,v2 ,v3 ,v4}.

  21. 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.

  22. 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.

  23. 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.

  24. } -predicates } domain predicates Predicates EDB predicates IDB predicates v1(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)

  25. 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.

  26. v2(A, B, C) B v1(A, C) v3(C, D) C A D v4(C,E) v5(E, F) E F f-closure({A},{v1,v2,v3}) = {v1,v2,v3} f-closure({D},{v1,v2,v3}) = {} Forward-closure Given 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.

  27. v2(A, B, C) B v1(A, C) v3(C, D) C A D v4(C,E) v5(E, F) E F Backward-closure • Backward-closure of a set of attributes X: b-closure(X), is the set of views that can help retrieve bindings for X. b-closure(C) = {v1,v2,v4} • Lemma: All backward-closures of a connection are • the same.

  28. free free free bound bound bound v2(A, B, C) B v1(A, C) v3(C, D) C A D v4(C,E) v5(E, F) E F BF-chain, backward-closure • BF-chain: • Backward-closure: b-closure(C) = {v1,v2,v4}

  29. 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.

  30. 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.

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