1. Ting Chen, Jiaheng Lu, Tok Wang Ling
On Boosting Holism in XML Twig Pattern Matching Using Structural Indexing Techniques
Ting Chen, Jiaheng Lu, Tok Wang Ling

2. Outline Background Our holistic Twig Pattern Matching algorithms
XML Twig Pattern Query
Previous Twig Join algorithms
Limit of the original holistic method TwigStack
Our holistic Twig Pattern Matching algorithms
Two Refined Indexing Schemes: Tag+Level and PPS
A generalized holistic matching theory
iTwigJoin: a generalized holistic matching algorithm
Experiments
Conclusion
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

3. Background: XML and Region coding
XML document is modeled as a tree in our work
Region Coding for XML document tree
<start, end, level> label for each element
Containment Property:
a.start < b.start AND a.end > b.end if and only if a is an ancestor of b
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

4. Background: XML twig pattern queries
An XML twig query is a small tree, whose edges include parent-child or ancestor-descendant relationships.
Given an XML document D, and an XML twig query Q, our problem is to find all occurrences of Q on D.
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

5. Previous XML Twig Join algorithms
Techniques
Edge Based
Binary Structural Join [Al-Khalifa et al ICDE02]
Join Order Selection [Wu et al ICDE03]
Path Based
BLAS [Chen et al SIGMOD04]
Tree (Holistic) Based
TwigStack [Bruno et al SIGMOD02]
TwigStackList [Lu et al CIKM04]
Index Based
B tree [[Chien et al VLDB02]
XR tree[Jiang et al ICDE02]
TSGeneric+[Jiang et al VLDB03]
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

6. Holistic Twig Matching
TwigStack [Bruno et al SIGMOD02] A holistic twig join algorithm
E.g: For query A[.//C]//B, there may be many matches only to A//B. But TwigStack only output results for A with descendants B and C.
No join order selection required
TwigStack is optimal for only ancestor-descendant twig patterns.
Reordering of elements in a stream does not help. [Choi et al DEXA03]
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

7. Sub-optimality of TwigStack
Not optimal for twigs with parent-child edge a1 a1
a2 … an A b1 a2 an cn B C b1
b2 … bn c1
c2 … cn … b2 c1 bn
cn-1
Document
Query
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

8. Two Refined Streaming Schemes(1)
To enlarge the optimality of TwigStack, in our paper we proposed two refined streaming schemes.
Tag + Level: elements with the same tag and level are grouped together a1 A a1 … b1 a2 an cn b1 a2
a3 … an cn B C … b2
b3 … bn c1
c2 … b2 c1 bn
cn-1
Document
Query
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

9. Two Refined Streaming Schemes(1)
For this query, tag+level streaming scheme can guarantee the optimality. a1 A a1 … b1 a2 an cn b1 a2
a3 … an cn B C … b2
b3 … bn c1
c2 … b2 c1 bn
cn-1
Document
Query
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

10. Two Refined Streaming Schemes(1)
But given a more complex query and document, tag+level cannot guarantee the optimality. For example: a1 A a1 e1 a2 b2 a2 b2 D B d3 d1
d2,d3 d1 d2 b1 b1 C c1 c2
Query c1 c2
Document
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

11. Two Refined Streaming Schemes(2)
Prefix Path Streaming (PPS): elements with the same root-to-node path are grouped together
Every element in the document is stored as an individual stream in this example. D: a1 a1 e1 a2 b2 e1 a2 b2 d1 d2 b1 d3 d3 d1 d2 b1 c1 c2
Document c1 c2
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

12. Two Refined Streaming Schemes(2)
PPS is optimal for the following example.
d1,d2,c1,c2 are separated to different streams a1 A a1 e1 a2 b2 a2 b2 D B d3 d1 d2 d1 d2 b1 b1 C c1 c2
Query c1 c2
Document
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

13. Two Refined Streaming Schemes(2)
A natural question : Can PPS guarantee to be optimal for all queries and data?
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

14. Two Refined Streaming Schemes(2)
A natural question : Can PPS guarantee to be optimal for all queries and data?
The answer is NO.
For example:
c1, c2 are in the same stream. Similarly, e1, e2 are also in the same stream. A a1 b1 b2 b3 C B a2 a3 a4 d2 E D c1 c2 b4 b5 e1 d1 e2
Query
: head element
Document
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

15. A general algorithm: iTwigJoin
We propose a general algorithm, called iTwigJoin , which can be used on various data streaming schemes.
Our key idea is to classify all current head elements to three classes:
Subtree-matching
Useless
Blocked
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

16. Classifying Head Elements
Subtree-Matching Element
Element e of tag E is called a subtree-matching element for query Q
e is in a match to QE (QE is the sub-tree of Q rooted at E); and
NOT in any future match to QP where P is the parent of E in Q
Useless Element
Element e is called a useless element if e is not in any future match to QE.
Blocked Element
An element which is neither subtree-matching nor useless
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

17. Example: Classifying Head Elements (Tag+Level Streaming)
Q1: e1 a2 b2 D B d1 d2 b1 d3 C c1 c2
: head element a1 a2 b2 d1
d2 d3 … b1 c1 c2
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

18. Example: Classifying Head Elements (Tag+Level Streaming)
Q1:
Subtree-matching
useless
blocked d1 e1 a2 b2 D B d1 d2 b1 d3 C c1 c2
: head element a1 a2 b2 d1
d2 d3 … b1 c1 c2
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

19. Example: Classifying Head Elements (Tag+Level Streaming)
Q1:
Subtree-matching
useless
blocked
d1,c1 e1 a2 b2 D B d1 d2 b1 d3 C c1 c2
: head element a1 a2 b2 d1
d2 d3 … b1 c1 c2
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

20. Example: Classifying Head Elements (Tag+Level Streaming)
Q1:
Subtree-matching -
useless
blocked
d1,c1,a1,a2,b2,b1 e1 a2 b2 D B d1 d2 b1 d3 C c1 c2
: head element a1 a2 b2 d1
d2 d3 … b1 c1 c2
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

21. Example: Classifying Head Elements (Tag+Level Streaming)
Q1:
Subtree-matching -
useless
blocked
d1,c1,a1,a2,b2,b1 e1 a2 b2 D B d1 d2 b1 d3 C c1 c2
: head element a1
Q2: A a2 b2
Subtree-matching
useless
blocked D B d1
d2 d3 … b1 c1 c2 C
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

22. Example: Classifying Head Elements (Tag+Level Streaming)
Q1:
Subtree-matching -
useless
blocked
d1,c1, a1,a2,b2,b1 e1 a2 b2 D B d1 d2 b1 d3 C c1 c2
: head element a1
Q2: A a2 b2
Subtree-matching d1
useless
blocked D B d1
d2 d3 … b1 c1 c2 C
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

23. Example: Classifying Head Elements (Tag+Level Streaming)
Q1:
Subtree-matching -
useless
blocked
d1,c1, a1,a2,b2,b1 e1 a2 b2 D B d1 d2 b1 d3 C c1 c2
: head element a1
Q2: A a2 b2
Subtree-matching d1
useless
a1,b2
blocked D B d1
d2 d3 … b1 c1 c2 C
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

24. Example: Classifying Head Elements (Tag+Level Streaming)
Q1:
Subtree-matching -
useless
blocked
d1,c1, a1,a2,b2,b1 e1 a2 b2 D B d1 d2 b1 d3 C c1 c2
: head element a1
Q2: A a2 b2
Subtree-matching d1
useless
a1,b2
blocked c1 D B d1
d2 d3 … b1 c1 c2 C
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

25. Example: Classifying Head Elements (Tag+Level Streaming)
Q1:
Subtree-matching -
useless
blocked
d1,c1, a1,a2,b2,b1 e1 a2 b2 D B d1 d2 b1 d3 C c1 c2
: head element a1
Q2: A a2 b2
Subtree-matching d1
useless
a1,b2
blocked
c1, b1, a2, D B d1
d2 d3 … b1 c1 c2 C
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

26. Example: Classifying Head Elements (Tag+Level Streaming)
Subtree-matching -
useless
blocked
a1,a2,b1,b2,c1,d1 e1 a2 b2 D B A C d1 d2 b1 d3 B D
Subtree-matching
d1,
useless
a1,b2
blocked
a2,b1,c1 C c1 c2
Useless element can be discarded safely
sub-tree Matching element is pushed to the corresponding stack
Blocked element causes problem
CANNOT be discarded because it may cause loss of results
CANNOT be pushed to stack because it may cause useless results
When all head elements are blocked; optimal holistic matching CANNOT be guaranteed
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

27. iTwigJoin
In our algorithm, in order to output all correct answers, we push blocked elements into stack, which may result in useless intermediate results in some cases.
Tag+Level Streaming a1 A
Q1: e1 a2 b2 D B d1 d2 b1 d3 C c1 c2
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

28. iTwigJoin
In our algorithm, in order to output all correct answers, we push blocked elements into stack, which may result in useless intermediate results in some cases.
Tag+Level Streaming a1
Since all head elements are blocked, we have to push a1 to stack and output one path solution (a1,d1). A
Q1: e1 a2 b2 D B d1 d2 b1 d3 C c1 c2
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

29. If there is no c2, then (a1,d1) is a useless path solution.
iTwigJoin
In our algorithm, in order to output all correct answers, we push blocked elements into stack, which may result in useless intermediate results in some cases.
Tag+Level Streaming a1
Since all head elements are blocked, we have to push a1 to stack and output one path solution (a1,d1). A
Q1: e1 a2 b2 D B d1 d2 b1 d3 C c1 c2
If there is no c2, then (a1,d1) is a useless path solution.
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

30. iTwigJoin Two Main Components
Stream Manager: Control the advance operation of streams and send elements for temporary storage
Temporary Storage: Push elements to stack and output intermediate paths.
Stream Manager
Temporary Storage a1 SA a2 b2 SB SC c1
c2 c3 … b1
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

31. Flowchart of iTwigJoin
Label current head elements
as either subtree-Matching, Useless or Blocked
If useless element is found
Discard Useless elements
If not all streams end
Select a subtree-Matching or blocked element e
Pop some elements from stack
Push e to the stack and output
intermediate paths if e is the leaf
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

32. Optimal classes of iTwigJoin for three streaming schemes
Tag Streaming
A-D only pattern
A-D only
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

33. Optimal classes of iTwigJoin for three streaming schemes
Tag Streaming
A-D only pattern
Tag+Level Streaming
A-D/P-C only pattern
A-D/P-C only
A-D only
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

34. Optimal classes of iTwigJoin for three streaming schemes
Tag Streaming
A-D only pattern
Tag+Level Streaming
A-D/P-C only pattern
Prefix Path Streaming
A-D/P-C only or 1-Branch
A-D/P-C only or 1-Branch node
A-D/P-C only
A-D only
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

35. Optimal classes of iTwigJoin for three streaming schemes
Optimal class:Larger
More refined
Tag Streaming
A-D only pattern
Tag+Level Streaming
A-D/P-C only pattern
Prefix Path Streaming
A-D/P-C only or 1-Branch
A-D/P-C only or 1-Branch node
A-D/P-C only
A-D only
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

36. Experiments Benchmarks XMark: Synthetic Data
Treebank: Real Data from Wall Street Journal
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

37. Experiments: I/O Performance
Tree1: A-D only
Tree2: P-C only
Tree3: P-C only
Tree4: 1-branchnode
Tree5: 1-branchnode
By pruning irrelevant streams, PPS usually scan the fewest number of elements.
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

38. Experiments: Number of Intermediate Paths
Tree1: A-D only
Tree2: P-C only
Tree3: P-C only
Tree4: 1-branchnode
Tree5: 1-branchnode
For treebank 5, there is no matching results. So Tag+Level and PPS do not output any intermediate results.
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

39. Experiments: Running Time
XMark1: Path Pattern,
XMark2: A-D only,
XMark3: P-C only,
XMark4: 1-branchnode,
XMark5: Non-optimal,
Tag+level and PPS have better performance than TwigStack and TwigStackList in XMark data.
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

40. Experiments: Summary
Both PPS and Tag+Level help to reduce I/O costs. while PPS saves more.
PPS may result in too many streams for deep XML data; Tag+Level seems to be a good compromise.
PPS and Tag+Level completely avoid the output of redundant intermediate paths in all cases we tested, though they cannot guarantee the optimality in theory.
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

41. Conclusions
We develop a general algorithm to perform holistic twig join on Tag+Level and PPS streaming schemes.
We identify two I/O optimal classes for Tag+Level and PPS streaming schemes.
Since our experiments show that Tag+Level streaming schemes can guarantee to produce very few useless intermediate results in most cases, we recommend to use Tag+Level scheme for efficient XML twig pattern matching.
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

42. END
Thank you!
Q & A
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

43. Backup iTwigJoin Algorithm
While(not all streams end)
Label current head elements as either Matching, Useless or Blocked
If any head element is Useless, discard it and continue
Let e1 be the matching element with the smallest startPos;
Let e2 be the blocked element with the smallest endPos;
If e2.endPos < e1.startPos, let e be the blocked element with
the smallest startPos; else let e be e1
Advance the stream e belongs to
Pop out elements from e’s stack whose endPos < e.startPos
Push e into its stack if e has a parent/ancestor in the temporary storage system,
Output all paths involving e If the tag of e is a leaf node in Q
On Boosting Holism in XML Twig Pattern Matching using Structural Indexing