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1
Debugging Schema Mappings
with Routes
Laura ChiticariuUC Santa Cruz
(joint work with Wang-Chiew Tan)
2
SPIDER: A Schema Mapping Debugger
Today 14:00-15:30 Thursday 11:00-12:30
Demo group B
3
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
Schema S Schema T
I
Source instance
J
Target instance
M
4
Debugging a Data Exchange Today
XQuery/XSLT/Java
Debugging at the (low) level of the implementation1. Specific to the data exchange engine2. Specific to the implementation language: XQuery, SQL, etc
Debugging at the level of schema mappings
NO SUPPORT!!!
Schema S Schema T
I
Source instance
J
Target instance
M
5
Debugging Schema Mappings
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
I
Source instance
J
Target instance
M
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)
8 x ((x) ! 9 y (x,y)) Equality generating dependencies (egds)
8 x ((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
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
I
Source instance
J
Target instance
10
Example Schema Mapping
Source-to-target dependencies, st:m1: CardHolders(cn,l,s,n) ! 9L (Accounts(cn,L,s) Æ Clients(s,n))
m2: Dependents(an,s,n) ! Clients(s,n)
Target dependencies, t:m3: Clients(s,n) ! 9A 9L (Accounts(A,L,s))
MANHATTAN CREDITCardHolders: cardNo ² limit ² ssn ² name ²
Dependents: accNo ² ssn ² name ²
FARGO FINANCEAccounts:² accNo² creditLine² accHolder
Clients:² ssn² name
m2
m1
m3
S: T:
Source instance I Target instance J Solution for I underthe schema mapping
123 $15K ID1 Alice
CardHolders
123 ID2 Bob
Dependents
123 L1 ID1
A2 L2 ID2
AccountsID1 Alice
ID2 Bob
Clients
fk1
11
Example Debugging Scenario 1
Unknown credit limit?
15K is not copied over to the target
Source instance I Target instance J
123 $15K ID1 Alice
CardHolders
123 ID2 Bob
Dependents
123 L1 ID1
A2 L2 ID2
AccountsID1 Alice
ID2 Bob
Clients
AliceID1$15K123
CardHolders ID1L1123
Accounts
AliceID1
Clientsm1
A route for the Accounts tuple
m1: CardHolders(cn,l,s,n) ! 9L (Accounts(cn,L,s) ^ Clients(s,n))
12
Example Debugging Scenario 1
Unknown credit limit?
15K is not copied over to the target
Source instance I Target instance J
123 $15K ID1 Alice
CardHolders
123 ID2 Bob
Dependents
123 L1 ID1
A2 L2 ID2
AccountsID1 Alice
ID2 Bob
Clients
AliceID1$15K123
CardHolders ID1L1123
Accounts
AliceID1
Clientsm1
A route for the Accounts tuple
m1: CardHolders(cn,l,s,n) ! (Accounts(cn,l,s) ^ Clients(s,n))
13
Example Debugging Scenario 2
Unknown account number?
123 is not copied over to the target as Bob’s account number
Source instance I Target instance J
123 $15K ID1 Alice
CardHolders
123 ID2 Bob
Dependents
123 L1 ID1
A2 L2 ID2
AccountsID1 Alice
ID2 Bob
Clients
m2BobID2123
Dependents
ID2L2A2
Accounts
BobID2
Clients m3
Route for Accounts tuple with accNo A2
m2: Dependents(an,s,n) ! Clients(s,n)
14
Example Debugging Scenario 2
Unknown account number?
123 is not copied over to the target as Bob’s account number
Source instance I Target instance J
123 $15K ID1 Alice
CardHolders
123 ID2 Bob
Dependents
123 L1 ID1
A2 L2 ID2
AccountsID1 Alice
ID2 Bob
Clients
m2BobID2123
Dependents
ID2L2A2
Accounts
BobID2
Clients m3
Route for Accounts tuple with accNo A2
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 Js µ 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: Ji µ J, mi 2 st [ t, where 1· i· n Js µ Jn
m1, h1 m2, h2mn, hn
16
Example of Satisfaction Step
123 $15K ID1 Alice
CardHolders123 L1 ID1
Accounts
ID1 Alice
Clients
m1, h1
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}
Unknown credit limit?
Source instance I Target instance J
123 $15K ID1 Alice
CardHolders
123 ID2 Bob
Dependents
123 L1 ID1
A2 L2 ID2
AccountsID1 Alice
ID2 Bob
Clients
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 Js µ 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
Compute all routes: A simple example 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)
T7(a)
T4(a) T6(a)
6, x a
19
Compute all routes: A simple example 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)
T7(a)
T4(a) T6(a)
6
T3(a)
4, x a
20
Compute all routes: A simple example 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)
T7(a)
T4(a) T6(a)
6
T3(a)
4
T5(a)
7
21
Compute all routes: A simple example 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)
T7(a)
T4(a) T6(a)
6
T3(a)
T5(a)
4
7
T4(a) T1(a)
5
S1(a)
1
22
Compute all routes: A simple example 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)
T7(a)
T4(a) T6(a)
6
T3(a)
T5(a)
4
7
S2(a)
2
T4(a) T1(a)
5
T2(a)
S2(a)
3
2
S1(a)
1
23
Compute all routes: A simple example 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)
T7(a)
T4(a) T6(a)
6
T3(a)
T5(a)
4
7
S2(a)
8
T4(a) T1(a)
5
T2(a)
S2(a)
3
2
S1(a)
1
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
SQL Schema mappings
Eager DBNotes [B.TV04] Mondrian [GKM06]
MXQL system[VMM05]
Lazy [CWW00][CW00a, CW00b]
Our routes approach
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
TGDs with 1 join in the LHS and RHS Routes with 3 satisfaction steps for each selected tuple
0
2
4
6
8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
# selected target tuples
Co
mp
ute
on
e ro
ute
(s
ec)
I:10MB; J:60MB I:50MB; J:300MB I:100MB; J:600MB
30
ComputeOneRoute with Rel. schema mappingInfluence of the Complexity of st [ t
TGDs with 0 to 3 joins in the LHS and RHSRoutes with 3 satisfaction steps for each selected tuple
Size of I = 100MB, Size of J = 600MB
0
5
10
15
20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
# selected target tuples
Co
mp
ute
on
e
rou
te (
sec)
no joins 1 join 2 joins 3 joins
31
ComputeOneRoute vs. ComputeAllRoutes
TGDs with 1 join in the LHS and RHSRoutes with 3 satisfaction steps
Size of I = 100MB, Size of J = 600MB
0.0010.010.1
110
1001000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
# selected target tuples
Ru
nn
ing
tim
e (s
ec)
computeOneRoute computeAllRoutes
32
Experimental results with Mondial, DBLP and AmalgamSchemas Total
Elem.AtomicElems.
Nest.Depth
Inst. Size
|st|/|t|
S DBLP1 (XML) 65 57 1 640KB 10/14
DBLP2 (XML) 20 12 4 850KB
T Amalgam (rel) 117 100 1 1.1MB
S Mondial1 (rel) 157 129 1 1 MB 13/25
T Mondial2 (XML) 144 112 4 1.2MB
33
Experimental results with Mondial, DBLP and AmalgamSchemas Total
Elem.AtomicElems.
Nest.Depth
Inst. Size
|st|/|t|
S DBLP1 (XML) 65 57 1 640KB 10/14
DBLP2 (XML) 20 12 4 850KB
T Amalgam (rel) 117 100 1 1.1MB
S Mondial1 (rel) 157 129 1 1 MB 13/25
T Mondial2 (XML) 144 112 4 1.2MB
Two DBLP schemas and datasets, both XML: DBLP1, DBLP2
First relational schema from Amalgam test suite
34
Experimental results with Mondial, DBLP and AmalgamSchemas Total
Elem.AtomicElems.
Nest.Depth
Inst. Size
|st|/|t|
S DBLP1 (XML) 65 57 1 640KB 10/14
DBLP2 (XML) 20 12 4 850KB
T Amalgam (rel) 117 100 1 1.1MB
S Mondial1 (rel) 157 129 1 1 MB 13/25
T Mondial2 (XML) 144 112 4 1.2MB
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 AmalgamSchemas Total
Elem.AtomicElems.
Nest.Depth
Inst. Size
|st|/|t|
S DBLP1 (XML) 65 57 1 640KB 10/14
DBLP2 (XML) 20 12 4 850KB
T Amalgam (rel) 117 100 1 1.1MB
S Mondial1 (rel) 157 129 1 1 MB 13/25
T Mondial2 (XML) 144 112 4 1.2MB
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
SPIDER: A Schema Mappings Debugger
Compute one/all routes Alternative routes Guided computation of
routes Standard debugging
features Breakpoints “Watch” windows
Schema-level routes
Today 14:00-15:30 Thursday 11:00-12:30
Demo group B
38
Thank you!