Containment of Partially Specified Tree-Pattern Queries
description
Transcript of Containment of Partially Specified Tree-Pattern Queries
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Containment of Partially Specified
Tree-Pattern QueriesDimitri Theodoratos (NJIT, USA)
Theodore Dalamagas (NTUA, GREECE)
Pawel Placek (NJIT, USA)
Stefanos Souldatos (NTUA, GREECE)
Timos Sellis (NTUA, GREECE)
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Introduction
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Stefanos Souldatos - SSDBM 2006 3
Motivating example Consider a database including shops that sell
spare parts for motorbikes. The authors of the paper need spare parts for
their motorbikes. BUT… rr
ATHENSATHENS
HONDAHONDA
GREECEGREECE USAUSA
YAMAHAYAMAHA BMWBMW
TRAVELTRAVEL
VARADEROVARADERO
125cc125cc 1000cc1000cc
ON-OFFON-OFF
200cc200cc
SERROWSERROW
TRAVELTRAVEL
650cc650cc
F650F650F650GSF650GS
YAMAHAYAMAHA BMWBMW
ON-OFFON-OFF
200cc200cc
SERROWSERROW
TRAVELTRAVEL
F650GSF650GS
650cc650cc
NJNJ
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1: Structural Differences Dimitri Theodoratos lives in NY. He owns a
Yamaha Serrow motorbike in Greece. So, he searches for spare parts in Greece or USA.
A structural difference emerges…
rr
ATHENSATHENS
HONDAHONDA
GREECEGREECE USAUSA
YAMAHAYAMAHA BMWBMW
TRAVELTRAVEL
VARADEROVARADERO
125cc125cc 1000cc1000cc
ON-OFFON-OFF
200cc200cc
SERROWSERROW
TRAVELTRAVEL
650cc650cc
F650F650F650GSF650GS
YAMAHAYAMAHA BMWBMW
ON-OFFON-OFF
200cc200cc
SERROWSERROW
TRAVELTRAVEL
F650GSF650GS
650cc650cc
NJNJ
?
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Stefanos Souldatos - SSDBM 2006 5
2: Structural Inconsistencies Theodore Dalamagas owns a BMW motorbike
and looks for spare parts worldwide. A structural inconsistency emerges…
rr
ATHENSATHENS
HONDAHONDA
GREECEGREECE USAUSA
YAMAHAYAMAHA BMWBMW
TRAVELTRAVEL
VARADEROVARADERO
125cc125cc 1000cc1000cc
ON-OFFON-OFF
200cc200cc
SERROWSERROW
TRAVELTRAVEL
650cc650cc
F650F650F650GSF650GS
YAMAHAYAMAHA BMWBMW
ON-OFFON-OFF
200cc200cc
SERROWSERROW
TRAVELTRAVEL
F650GSF650GS
650cc650cc
NJNJ
650cc/F650GS
vs
F650GS/650cc
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3: Unknown Structure Stefanos Souldatos owns a Honda Varadero. But, he is not fully aware of the hierarchy...
rr
ATHENSATHENS
HONDAHONDA
GREECEGREECE USAUSA
YAMAHAYAMAHA BMWBMW
TRAVELTRAVEL
VARADEROVARADERO
125cc125cc 1000cc1000cc
ON-OFFON-OFF
200cc200cc
SERROWSERROW
TRAVELTRAVEL
650cc650cc
F650F650F650GSF650GS
YAMAHAYAMAHA BMWBMW
ON-OFFON-OFF
200cc200cc
SERROWSERROW
TRAVELTRAVEL
F650GSF650GS
650cc650cc
NJNJ
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rr
ATHENSATHENS
HONDAHONDA
GREECEGREECE USAUSA
YAMAHAYAMAHA BMWBMW
TRAVELTRAVEL
VARADEROVARADERO
125cc125cc 1000cc1000cc
ON-OFFON-OFF
200cc200cc
SERROWSERROW
TRAVELTRAVEL
650cc650cc
F650F650F650GSF650GS
YAMAHAYAMAHA BMWBMW
ON-OFFON-OFF
200cc200cc
SERROWSERROW
TRAVELTRAVEL
F650GSF650GS
650cc650cc
NJNJ
4: Source Integration Pawel Placek wants to buy a motorbike that he
can easily find spare parts for. He searches in many hierarchies with different
structure…rr
ATHENSATHENS
HONDAHONDA
GREECEGREECE USAUSA
YAMAHAYAMAHA BMWBMW
TRAVELTRAVEL
VARADEROVARADERO
125cc125cc 1000cc1000cc
ON-OFFON-OFF
200cc200cc
SERROWSERROW
TRAVELTRAVEL
650cc650cc
F650F650F650GSF650GS
YAMAHAYAMAHA BMWBMW
ON-OFFON-OFF
200cc200cc
SERROWSERROW
TRAVELTRAVEL
F650GSF650GS
650cc650cc
NJNJ
rr
ATHENSATHENS
HONDAHONDA
GREECEGREECE USAUSA
YAMAHAYAMAHA BMWBMW
TRAVELTRAVEL
VARADEROVARADERO
125cc125cc 1000cc1000cc
ON-OFFON-OFF
200cc200cc
SERROWSERROW
TRAVELTRAVEL
650cc650cc
F650F650F650GSF650GS
YAMAHAYAMAHA BMWBMW
ON-OFFON-OFF
200cc200cc
SERROWSERROW
TRAVELTRAVEL
F650GSF650GS
650cc650cc
NJNJ
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Stefanos Souldatos - SSDBM 2006 8
Motivation Querying tree-structured data requires exact
knowledge of the structure. BUT, structure is not always strictly defined!
MOREOVER, the user needs to set queries without always dealing with structure: Find shops for Honda spare parts in Athens, Greece …where Athens is a descendant of Greece …but I don’t know if Athens is an ancestor or a
descendant of Honda.
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Previous Approaches Keyword-based search approach
Total absence of structure. Approximation techniques
Relax the initial query and retrieve more answers. Naive approach
All possible query patterns are generated and evaluated against the tree structure.
Traditional integration approach Global structure and mapping rules.
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Our Approach We have designed a Query Language that
allows for partial specification of the structure (Partially Specified Tree-Pattern Queries).
Query formulation and evaluation is based on Dimension Graphs that summarize the structure of the trees.
Dimension graphs group sets of semantically related nodes called Dimensions.
We study the problem of Query Containment for Partially Specified Tree-Pattern Queries.
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Data Model
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Dimension Graphs
Dimension graphs summarize the structure of the tree.
rr
ATHENSATHENS
HONDAHONDA
GREECEGREECE USAUSA
YAMAHAYAMAHA BMWBMW
TRAVELTRAVEL
VARADEROVARADERO
125cc125cc 1000cc1000cc
ON-OFFON-OFF
200cc200cc
SERROWSERROW
TRAVELTRAVEL
650cc650cc
F650F650F650GSF650GS
YAMAHAYAMAHA BMWBMW
ON-OFFON-OFF
200cc200cc
SERROWSERROW
TRAVELTRAVEL
F650GSF650GS
650cc650cc
NJNJ
R (oot)
C (ountry) = {GREECE, USA}
B (rand)
T (ype)
L (ocation)
M (odel)
E (ngine)
R
C
B
T M
L
E
DIMENSIONS
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Dimension Graphs…
Offer a summary of the structure of the tree.
Provide the necessary semantics for query formulation.
Set the framework for querying sources with structural differences and inconsistencies.
Support query evaluation and optimization.
R
C
B
T M
L
E
R (oot)
C (ountry)
B (rand)
T (ype)
L (ocation)
M (odel)
E (ngine)
DIMENSIONS
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Partially Specified Tree-pattern Queries
Query: Find shops with spare parts for all models and engines of BMW motorbikes in Greece.
R
C
B
T M
L
E
C = {Greece}
B = {BMW}
M = ?
B = {BMW}
E = ?
R (oot)
C (ountry)
B (rand)
T (ype)
L (ocation)
M (odel)
E (ngine)
DIMENSIONS
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Partially Specified Tree-pattern Queries
Query: Find shops with spare parts for all models and engines of BMW motorbikes in Greece.
R
C
B
T M
L
E
partially specified paths (PSP)
C = {Greece}
B = {BMW}
M = ?
B = {BMW}
E = ?
PSP *p2PSP p1R (oot)
C (ountry)
B (rand)
T (ype)
L (ocation)
M (odel)
E (ngine)
DIMENSIONS
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Partially-Specified Tree-pattern Queries
Query: Find shops with spare parts for all models and engines of BMW motorbikes in Greece.
R
C
B
T M
L
E
output path (*)
partially specified paths (PSP)
C = {Greece}
B = {BMW}
M = ?
B = {BMW}
E = ?
PSP *p2PSP p1R (oot)
C (ountry)
B (rand)
T (ype)
L (ocation)
M (odel)
E (ngine)
DIMENSIONS
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Partially-Specified Tree-pattern Queries
Query: Find shops with spare parts for all models and engines of BMW motorbikes in Greece.
parentchild
R
C
B
T M
L
E
output path (*)
partially specified paths (PSP)
ancestordescendant
C = {Greece}
B = {BMW}
M = ?
B = {BMW}
E = ?
PSP *p2PSP p1R (oot)
C (ountry)
B (rand)
T (ype)
L (ocation)
M (odel)
E (ngine)
DIMENSIONS
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Partially-Specified Tree-pattern Queries
Query: Find shops with spare parts for all models and engines of BMW motorbikes in Greece.
parentchild
R
C
B
T M
L
E
node sharing expression
(NSE)
output path (*)
partially specified paths (PSP)
ancestordescendant
C = {Greece}
B = {BMW}
M = ?
B = {BMW}
E = ?
PSP *p2PSP p1R (oot)
C (ountry)
B (rand)
T (ype)
L (ocation)
M (odel)
E (ngine)
DIMENSIONS
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Dimension Trees and Query Evaluation
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Dimension TreesR
C
B
T M
L
E
1) We apply Inference Rules to the query to produce its Full Form.
2) We search for paths in the graph that match the paths of the query.
3) Paths in the graph correspond to Dimension Trees.
4) Dimension trees are translated into XPath queries.
C = {Greece}
B = {BMW}
M = ?
B = {BMW}
E = ?
PSP *p2PSP p1
C = {Greece}
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Stefanos Souldatos - SSDBM 2006 21
Dimension TreesR
C
B
T M
L
E
1) We apply Inference Rules to the query to produce its Full Form.
2) We search for paths in the graph that match the paths of the query.
3) Paths in the graph correspond to Dimension Trees.
4) Dimension trees are translated into XPath queries.
C = {Greece}
B = {BMW}
M = ?
B = {BMW}
E = ?
PSP *p2PSP p1
C = {Greece}
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Stefanos Souldatos - SSDBM 2006 22
Dimension TreesR
C
B
T M
L
E
1) We apply Inference Rules to the query to produce its Full Form.
2) We search for paths in the graph that match the paths of the query.
3) Paths in the graph correspond to Dimension Trees.
4) Dimension trees are translated into XPath queries.
RC = {Greece}
B = {BMW}
T
ME
C = {Greece}
B = {BMW}
M = ?
B = {BMW}
E = ?
PSP *p2PSP p1
C = {Greece}
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Stefanos Souldatos - SSDBM 2006 23
Dimension TreesR
C
B
T M
L
E
r/Greece/BMW/*T[*E]/*M
1) We apply Inference Rules to the query to produce its Full Form.
2) We search for paths in the graph that match the paths of the query.
3) Paths in the graph correspond to Dimension Trees.
4) Dimension trees are translated into XPath queries.
RC = {Greece}
B = {BMW}
T
ME
C = {Greece}
B = {BMW}
M = ?
B = {BMW}
E = ?
PSP *p2PSP p1
C = {Greece}
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Dimension TreesR
C
B
T M
L
E
So, Dimension Trees are equivalent to the Query in a specific Dimension Graph:
“Dimension Trees = Query + Graph”
RC = {Greece}
B = {BMW}
T
ME
C = {Greece}
B = {BMW}
M = ?
B = {BMW}
E = ?
PSP *p2PSP p1
C = {Greece}
r/Greece/BMW/*T[*E]/*M
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Query Containment
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Query Containment
Absolute Containment Query Q1 is absolutely contained in query Q2 if
the answers of Q1 in every dimension graph are also answers of Q2.
Relative Containment (with respect to graph) Query Q1 is contained in query Q2 with respect to
graph G if the answers of Q1 in G are also answers of Q2 in G.
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Query Containment
Absolute Containment Query Q1 is absolutely contained in query Q2 if
the answers of Q1 in every dimension graph are also answers of Q2.
Relative Containment (with respect to graph) Query Q1 is contained in query Q2 with respect to
graph G if the answers of Q1 in G are also answers of Q2 in G.
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Checking Absolute Containment
Query Q1 is absolutely contained in query Q2 if there is a mapping from Q2 to Q1.
Q1 Q2
C = ?
B = ?
M = ?
B = ?
E = ?
PSP p2PSP *p1
C = ? C = ?
B = ?E = ?
PSP p4PSP *p3
C = ?
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Checking Relative Containment
Query Q1 is contained in query Q2 with respect to graph G if every dimension tree of Q1 is contained in a dimension tree of Q2.
RC
B
T
ME
RC
B
T
E
A dimension tree of Q1 A dimension tree of Q2
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Absolute & Relative Containment Checking Absolute Containment:
1msec
Checking Relative Containment: 100msec – 1sec
We suggest a technique that improves the performance of Relative Containment check. (Relative Containment 2 – RC2)
It is a sound but not complete technique However, it maintains high accuracy for containment
check.
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Stefanos Souldatos - SSDBM 2006 31
Relative Containment 2 (RC2)
For each possible parent-child or ancestor-descendant relation in the query, we extract relations that hold in all graph paths that include it:
R=>C : RC
LB : RC, CL
We add these relations in Q1 and check absolutely whether Q1’ Q2.
R
C
B
T M
L
E
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Example Q1 is NOT absolutely contained in Q2. But, Q1 is relatively contained in Q2.
Q1 Q2
L = ?
B = ?
PSP *p1 PSP *p2
L = ?
C = ?
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Example Q1 is NOT absolutely contained in Q2. But, Q1 is relatively contained in Q2.
Q1 Q2
L = ?
B = ?
PSP *p1
L = ?
PSP *p2
C = ?
Relative Containment 2 LB : RC, CL
C = ?
R = ?
G
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Experiments
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Experiments We measured…
execution time for checking Absolute Containment, Relative Containment and Relative Containment 2 (RC2)
the accuracy of RC2
…varying the density of the dimension graphs (dimensions,
root-to-leaf paths) the size of the queries (PSPs, nodes per PSP)
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Varying Graphs
time (sec)
graph paths
Relative Containment
Relative Containment 2
Absolute Containment
RC2 accuracy > 80%
RC2 accuracy > 50%30 dimensions
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Varying Queries
time (sec)
dimensions per PSP
Relative Containment
Relative Containment 2
Absolute Containment
RC2 accuracy > 93%2 PSPs
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Conclusionand Future Work
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Conclusion We addressed the problem of Query
Containment for Partially Specified Tree-Pattern Queries (PSTPQs).
We suggested a sound technique for checking Relative Query Containment.
Experiments showed that the technique improves checking of relative containment one order of magnitude with accuracy over 80% for graphs of common sizes
(based on XML benchmarks e.g. XMark, XMach etc).
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Future Work Suggest and experiment with a set of heuristics
for checking Relative Query Containment. Discuss the trade-off between time and accuracy
for each of those heuristics.
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Questions?
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Stefanos Souldatos - SSDBM 2006 42
Links
Introduction (2-10)
Data Model (11-18)
Query Evaluation (19-24)
Query Containment (25-32)
Experiments (33-36)
Conclusion – Future Work (37-39)
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Appendix
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Stefanos Souldatos - SSDBM 2006 44
Dimension TreesR
C
B
T M
L
E
RC = {Greece}
B = {BMW}
T
M
E
r/Greece/BMW/
*T[*E]/*M
RC = {Greece}
B = {BMW}
T
ME
r/Greece/BMW/*T/*M [*E]
RC = {Greece}
B = {BMW}
T
E
M
RC = {Greece}
B = {BMW}
T
M
E
E
M
r/Greece/BMW/*T[*M/*E]/*E*M
r/Greece/BMW/*T/*E/*M
C = {Greece}
B = {BMW}
M = ?
B = {BMW}
E = ?
PSP *p2PSP p1
C = {Greece}