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Debugging Schema Mappings with Routes

Understand and refine schema mappings using test data at the schema level. Explore the process of debugging schema mappings with routes. Learn how to compute and optimize routes for data exchange systems.

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Debugging Schema Mappings with Routes

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  1. Debugging Schema Mappings with Routes Laura Chiticariu UC Santa Cruz (joint work with Wang-Chiew Tan)

  2. SPIDER: A Schema Mapping Debugger Demo group B Today 14:00-15:30 Thursday 11:00-12:30

  3. I Source instance Schema Mappings • A schema mapping is a logical assertion that describes the correspondence between two schemas • Key element in data exchange and data integration systems • Data Exchange [FKMP05] • Translate data conforming to a source schema S into data conforming to a target schema T so that the schema mapping M is satisfied M Schema S Schema T J Target instance

  4. I Source instance Debugging a Data Exchange Today M • Debugging at the (low) level of the implementation • Specific to the data exchange engine • Specific to the implementation language: XQuery, SQL, etc • Debugging at the level of schema mappings NO SUPPORT!!! Schema S Schema T XQuery/XSLT/Java J Target instance

  5. I Source instance Debugging Schema Mappings M • Debugging schema mappings: the process of exploring, understanding and refining a schema mapping through the use of (test) data at the level of schema mappings Schema S Schema T J Target instance

  6. Outline • Overview • Motivation • Debugging schema mappings with routes • Motivating example • What are routes? • Computing routes • Related work • Performance evaluation • Conclusions

  7. Motivation • Schema mappings are good • Higher-level, declarative programming constructs • Hide implementation details, allow for optimization • Typically easier to understand vs. SQL/XSLT/XQuery/Java • Serve a similar goal as model management [Bernstein03, MBHR05] • Uniformity in specifying and debugging • Reduce programming effort by allowing a user to specify and debug at the level of schema mappings • Schema mappings are often generated by schema matching tools • Close to user’s intention, but may need further refinements • Hard to understand without the help of tools

  8. Language for Schema Mappings • Tuple generating dependencies (tgds) • 8x ((x) !9y(x,y)) • Equality generating dependencies (egds) • 8x ((x) ! x1 = x2) • Remarks: • Widely used for relational schema mappings in data exchange and data integration [Kolaitis05,Lenzerini02] • TGDs generalize LAV, GAV and are equivalent to GLAV assertions in the terminology of data integration • Extended to handle XML data exchange [PVMHF02]

  9. I Source instance Relational Schema Mappings [FKMP03] • Schema mapping M = (S, T, st[t) • S, T: relational schemas with no relation symbols in common • Source-to-target dependencies st: • Source-to-target tgds (s-t tgds) S(x)!9y T(x,y) • Target dependencies t: • Target tgds: T(x)!9y T(x,y) • Target egds:  T(x)!x1 = x2 ∑st ∑t Schema S Schema T J Target instance

  10. Example Schema Mapping S: T: MANHATTAN CREDIT CardHolders: cardNo ² limit ² ssn ² name ² Dependents: accNo ² ssn ² name ² Source-to-target dependencies, st: m1: CardHolders(cn,l,s,n) ! 9L (Accounts(cn,L,s)  Clients(s,n)) m2: Dependents(an,s,n) ! Clients(s,n) Target dependencies,t: m3: Clients(s,n) !A L (Accounts(A,L,s)) FARGO FINANCE Accounts: ² accNo ² creditLine ² accHolder Clients: ² ssn ² name m1 fk1 m3 m2 Solution for I under the schema mapping Target instance J Source instance I CardHolders Accounts Clients Dependents

  11. Example Debugging Scenario 1 Target instance J Source instance I CardHolders Accounts Clients Dependents Unknown credit limit? A route for the Accounts tuple Accounts CardHolders 123 L1 ID1 m1 123 $15K ID1 Alice Clients ID1 Alice 15K is not copied over to the target m1: CardHolders(cn,l,s,n) ! 9L (Accounts(cn,L,s) ^ Clients(s,n))

  12. Example Debugging Scenario 1 Target instance J Source instance I CardHolders Accounts Clients Dependents Unknown credit limit? A route for the Accounts tuple Accounts CardHolders 123 L1 ID1 m1 123 $15K ID1 Alice Clients ID1 Alice 15K is not copied over to the target m1: CardHolders(cn,l,s,n) ! (Accounts(cn,l,s) ^ Clients(s,n))

  13. Route for Accounts tuple with accNo A2 Dependents Accounts Clients m2 m3 123 ID2 Bob ID2 Bob A2 L2 ID2 Example Debugging Scenario 2 Target instance J Source instance I CardHolders Accounts Clients Dependents Unknown account number? 123 is not copied over to the target as Bob’s account number m2: Dependents(an,s,n) ! Clients(s,n)

  14. Route for Accounts tuple with accNo A2 Dependents Accounts Clients m2 m3 123 ID2 Bob ID2 Bob A2 L2 ID2 Example Debugging Scenario 2 Target instance J Source instance I CardHolders Accounts Clients Dependents Unknown account number? 123 is not copied over to the target as Bob’s account number m’2: CardHolders(an,l,s’,n’)^ Dependents(an,s,n) ! Accounts(an,l,s)^ Clients(s,n)

  15. Debugging Schema Mappings with Routes • Main intuition: routes describe the relationships between source and target data with the schema mapping • Definition: Let: • M be a schema mapping • I be a source instance • J be a solution for I under M and Jsµ J A route for Js with M and (I,J) is a finite non-empty sequence of satisfaction steps (I,;) ! (I,J1) ! … ! (I,Jn) such that: • Jiµ J, mi2st [ t, where 1· i· n • Jsµ Jn mn, hn m1, h1 m2, h2

  16. Example of Satisfaction Step Target instance J Source instance I CardHolders Accounts Clients Dependents Unknown credit limit? Accounts CardHolders m1, h1 Clients m1: CardHolders(cn, l, s, n) !9L (Accounts(cn, L, s ) ^ Clients(s, n )) h1={cn ! ‘123’, l ! $15K, s ! ID1, n ! Alice, L ! L1}

  17. Compute all routes • The schema mapping M is fixed • Input: source instance I, a solution J for I under M, a set of target tuples Jsµ J • Output: a forest representing all routes for Js • Algorithm idea: • For each tuple t in Js, consider every possible 2st[t and h for witnessing t • Do the same for all target tuples encountered during the process until tuples from the source instance are obtained

  18. 6, x  a T4(a) T6(a) Compute all routes: A simple example T7(a) • st: • 1: S1(x) ! T1(x) • 2: S2(x) ! T2(x) Æ T6(x) • t: • 3: T2(x) ! T3(x) • 4: T3(x) ! T4(x) • 5: T4(x) Æ T1(x) ! T5(x) • 6: T4(x) Æ T6(x) ! T7(x) • 7: T5(x) ! T3(x) • Source instance, I: • S1(a), S2(a) • A solution, J: • T1(a), …, T7(a)

  19. 4, x  a T3(a) Compute all routes: A simple example T7(a) • st: • 1: S1(x) ! T1(x) • 2: S2(x) ! T2(x) Æ T6(x) • t: • 3: T2(x) ! T3(x) • 4: T3(x) ! T4(x) • 5: T4(x) Æ T1(x) ! T5(x) • 6: T4(x) Æ T6(x) ! T7(x) • 7: T5(x) ! T3(x) • Source instance, I: • S1(a), S2(a) • A solution, J: • T1(a), …, T7(a) 6 T4(a) T6(a)

  20. 7 T5(a) Compute all routes: A simple example T7(a) • st: • 1: S1(x) ! T1(x) • 2: S2(x) ! T2(x) Æ T6(x) • t: • 3: T2(x) ! T3(x) • 4: T3(x) ! T4(x) • 5: T4(x) Æ T1(x) ! T5(x) • 6: T4(x) Æ T6(x) ! T7(x) • 7: T5(x) ! T3(x) • Source instance, I: • S1(a), S2(a) • A solution, J: • T1(a), …, T7(a) 6 T4(a) T6(a) 4 T3(a)

  21. 5 T4(a) T1(a) 1 S1(a) Compute all routes: A simple example T7(a) • st: • 1: S1(x) ! T1(x) • 2: S2(x) ! T2(x) Æ T6(x) • t: • 3: T2(x) ! T3(x) • 4: T3(x) ! T4(x) • 5: T4(x) Æ T1(x) ! T5(x) • 6: T4(x) Æ T6(x) ! T7(x) • 7: T5(x) ! T3(x) • Source instance, I: • S1(a), S2(a) • A solution, J: • T1(a), …, T7(a) 6 T4(a) T6(a) 4 T3(a) 7 T5(a)

  22. 2 S2(a) 3 T2(a) 5 2 T4(a) T1(a) S2(a) 1 S1(a) Compute all routes: A simple example T7(a) • st: • 1: S1(x) ! T1(x) • 2: S2(x) ! T2(x) Æ T6(x) • t: • 3: T2(x) ! T3(x) • 4: T3(x) ! T4(x) • 5: T4(x) Æ T1(x) ! T5(x) • 6: T4(x) Æ T6(x) ! T7(x) • 7: T5(x) ! T3(x) • Source instance, I: • S1(a), S2(a) • A solution, J: • T1(a), …, T7(a) 6 T4(a) T6(a) 4 T3(a) 7 T5(a)

  23. 5 T4(a) T1(a) 1 S1(a) Compute all routes: A simple example T7(a) • st: • 1: S1(x) ! T1(x) • 2: S2(x) ! T2(x) Æ T6(x) • t: • 3: T2(x) ! T3(x) • 4: T3(x) ! T4(x) • 5: T4(x) Æ T1(x) ! T5(x) • 6: T4(x) Æ T6(x) ! T7(x) • 7: T5(x) ! T3(x) • Source instance, I: • S1(a), S2(a) • A solution, J: • T1(a), …, T7(a) 6 T4(a) T6(a) 4 8 T3(a) S2(a) 7 3 T5(a) T2(a) 2 S2(a) Route for T7(a): 2, 3, 4, 8, 6

  24. Properties of compute all routes • Completeness: Let F denote the route forest by our algorithm returned on Js. If R is a minimal route for Js, then it is represented in F. • Running time: polynomial in the sizes of I, J and Js • Every “branch of a tuple” once explored, is never explored again • Polynomial number of branches for each tuple since M is fixed • Challenge: • Exponentially many routes, but polynomial-size representation constructed in polynomial time

  25. Compute one route • Our experimental results indicate that compute all routes can be expensive • Generate one route fast and alternative routes as needed? • Our solution: adapt compute all routes to compute only one route • Non-exhaustive: Stops when one witness is found. A witness that uses source tuples is preferred • Inference procedure: to deduce all consequences of a proven tuple and avoid recomputation of “branches” • Key step for polynomial time analysis • Completeness: If there is a route for Js, then our algorithm will produce a route for Js

  26. Related work • Commercial data exchange systems • e.g., Altova MapForce, Stylus Studio • Use “lower-level” languages (e.g., XSLT, XQuery) to specify the exchange • Debugging is done at this low level • Source tuple centric • Data viewer [YMHF01] • Constructs an “example” source instance illustrative for the behavior of the schema mapping • Complementary to our approach • Works only for relational schema mappings

  27. Related work • Computing routes for target data is related to computing provenance (aka lineage) of data

  28. Empirical Evaluation • Implementation: on top of the Clio data exchange system from IBM Almaden Research Center • Scalable: push computation to the database • Handles relational and XML schema mappings [PVMHF02] • Testbed: • Created relational and XML schema mappings based on the TPCH schema • Created schema mappings based on Mondial, DBLP and Amalgam schemas • Methodology - measured the influence of: • The sizes of I, J and Js • The complexity of st[t • i.e., the number of tgds and the number of atoms in each tgd • Setup: P4 2.8GHz, 2Gb RAM, 256MB DB2 buffer pool • Our regret: No benchmark to base our comparisons

  29. ComputeOneRoute with Rel. schema mappingInfluence of the Sizes of I and J

  30. ComputeOneRoute with Rel. schema mappingInfluence of the Complexity of st[t

  31. ComputeOneRoute vs. ComputeAllRoutes

  32. Experimental results with Mondial, DBLP and Amalgam

  33. Experimental results with Mondial, DBLP and Amalgam • Two DBLP schemas and datasets, both XML: • DBLP1, DBLP2 • First relational schema from Amalgam test suite

  34. Experimental results with Mondial, DBLP and Amalgam • Two DBLP schemas and datasets, both XML: • DBLP1, DBLP2 • First relational schema from Amalgam test suite • Two Mondial schemas and datasets: • one relational (Mondial1), the other XML (Mondial2) • Designed st and used the foreign key constraints as t

  35. Experimental results with Mondial, DBLP and Amalgam • Compute one route: under 3 seconds for 1-10 randomly selected tuples • Compute all routes: can take much longer • 18 seconds to construct the route forest for 10 selected tuples in the target instance of Mondial • Compute one route took under 1 second

  36. Conclusions • Debugging schema mappings with routes • Complete, polynomial time algorithms for computing routes • Extension for routes for selected source data • Routes have declarative semantics, based on the logical satisfaction of tgds • What we don’t do: illustrate data merging • Future work: • Illustrate grouping semantics for nested schema mappings • Adapt target instance to changes in the schema mapping and data sources

  37. Compute one/all routes Alternative routes Guided computation of routes Standard debugging features Breakpoints “Watch” windows Schema-level routes SPIDER: A Schema Mappings Debugger Demo group B Today 14:00-15:30 Thursday 11:00-12:30

  38. Thank you!

  39. How do we do it? M Source schema S Target Schema T Schema mappings debugger Source instance I Target instance J routes Witness selected target data with source data and M

  40. How do we do it? M Source schema S Target Schema T Schema mappings debugger Source instance I Target instance J routes Illustrate consequences of selected source data with M

  41. Key Concept: ROUTES - describe the relationships between source and target data with the schema mapping M Source schema S Target Schema T Schema mappings debugger Source instance I Target instance J routes

  42. Data Data Schema Schema Clio Source Target • A semi-automatic schema mapping system • Supports user-guided mapping from source to target with constraints • Schema mapping language: a nested extension of tgds and egds • Automatically generate XQuery/SQL/XSLT scripts for the actual data transferring based on the schema mapping • Generates universal solutions under relational-to-relational schema mappings • Implemented our techniques on top of Clio, but… • Routes have declarative semantics • Independent of Clio’s transformation engine Mapping XQuery/SQL/XSLT

  43. Provenance information Q’ Related work • Computing routes for target data is related to computing provenance (aka lineage) of data Q

  44. Related work • Computing routes for target data is related to computing provenance (aka lineage) of data Q No reengineering of the query

  45. Provenance information Eager Q’ Related work • Approaches to computing provenance: • Eager: changes the transformation to carry provenance information • Requires re-engineering of Q to Q’. No subsequent source access or access to the definition of Q or Q’. • Lazy: does not • No re-engineering of Q. Subsequent source access and access to the definition of Q may be needed. Q

  46. Related work • Computing routes for target data is related to computing provenance (aka lineage) of data

  47. Programming Languages vs. Schema Mappings • Debugging programming languages vs. debugging schema mappings • Procedural PL • We may have a specification (e.g. compute x2 on input x) which completely determines the output • Well-defined notion of correct answer • The program is an implementation of the specification • If the correct answer is not obtained, there’s a bug – need to debug the implementation • However, the specification may also not be that concrete • E.g., build a visual interface for … • Functional PL • Debugging is performed by analyzing a trace of the execution • Declarative approach for debugging [Nilsson94] • Schema mapping IS the specification • Infinite number of solutions consistent with the schema mapping • Best we can do: look at the target instance – if something looks wrong (e.g., the clients’ names are not copied to the target) go back to the schema mapping and try to refine it (or debug it)

  48. Related Work: Computing Provenance of Data over SQL queries • Compute the provenance of relational data in a view in data warehouses [CWW2000] • The provenance of a tuple t in a view is described as the tuples in the base tables that witness the existence of t Provenance answered using two reverse queries: R(a,b) :- R(a,b) Æ S(b,c) Æ a=1 Æ c=3 S(a,b) :- R(a,b) Æ S(b,c) Æ a=1 Æ c=3 T View definition: T(a,c) :- R(a,b) Æ S(b,c) DB R S

  49. Related Work: Computing Provenance of data over SQL queries • DBNotes: an annotation management system for relational databases • Each data value has zero or more annotations • pSQL: a query language for propagating annotations • 3 propagation schemes: DEFAULT, DEFAULT-ALL, CUSTOM • By default, annotations propagate according to provenance • Eager approach: annotations propagate along with data as data is transformed through queries • Provenance information readily available in the output • Automatically trace the provenance and flow of data over multiple transformation steps • Systematically maintains provenance annotations that describe the exact location of data values DB1 DB2 Transformation: T(a,c):-R(a,b)ÆS(b,c) R S T

  50. Related Work: Computing the Provenance of Data over Schema Mappings • MXQL system over relational/XML schema mappings • Eager approach • Additional info about source schema elements and mappings that contribute to the creation of target data is propagated and stored • Our approach is lazy: no reengineering • Non-automatic approach for answering provenance • The additional info needs to be queried using MXQL • We automatically compute routes for selected data • Data involved in the transformation not considered • Our routes contain information about schema elements, dependencies and data involved

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