on boosting holism in xml twig pattern matching using structural indexing techniques ting chen,...

On Boosting Holism in XML Twig Pattern Matching Using

Structural Indexing Techniques

Ting Chen, Jiaheng Lu, Tok Wang Ling

On Boosting Holism in XML Twig Pattern Matching using Structural Indexing

2

Outline Background

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


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


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.


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]


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]


7

Sub-optimality of TwigStack Not optimal for twigs with parent-child edge

a1

b1 a2 an cn

b2 c1 bn cn-1…

a1 a2 … an

b1 b2 … bn c1 c2 … cn

A

B C

QueryDocument


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

b1 a2 an cn…

b2 c1 bn cn-1…

a1

a3 … an

b2 b3 … bn c1 c2 …

a2b1 cn

A

B C

QueryDocument


9

Two Refined Streaming Schemes(1) For this query, tag+level streaming scheme can guarantee the optimality.

a1

b1 a2 an cn…

b2 c1 bn cn-1…

a1

a3 … an

b2 b3 … bn c1 c2 …

a2b1 cn

A

B C

QueryDocument


10

Two Refined Streaming Schemes(1) But given a more complex query and document, tag+level cannot guarantee the optimality.For example:

a1

e1 a2 b2

d2 b1 d3

c2

a1

d1 d2,d3

a2 b2

A

D B

QueryDocument

Cd1

c1

b1

c1 c2


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Two Refined Streaming Schemes(2) Prefix Path Streaming (PPS): elements with the same root-to-node path are grouped together

a1

a2

d1

b2

Document

a1

e1 a2 b2

d2 b1 d3

c1

d1

D:

d2 b1

c1

d3

c2

Every element in the document is stored as an individual stream in this

example.

e1

c2


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Two Refined Streaming Schemes(2) PPS is optimal for the following example.

a1

e1 a2 b2

d2 b1 d3

c2

a1

d1

a2 b2

A

D B

QueryDocument

Cd1

c1

b1

c1

d2

c2

d1,d2,c1,c2 are separated to

different streams


13

Two Refined Streaming Schemes(2) A natural question : Can PPS guarantee to be

optimal for all queries and data?


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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:

a1

b1 b2 b3

c2

a3

b5

a4

b4

a2

c1

e1 d1 e2

d2

A

C B

E D

c1, c2 are in the same stream.

Similarly, e1, e2 are also in the same

stream.

DocumentQuery: head element


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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


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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


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Example: Classifying Head Elements (Tag+Level Streaming)a1

e1 a2 b2

d2 b1

c2

d3

c1

d1

a1

d1 d2 d3 … b1

a2 b2

c1 c2

A

D B

C

D:Q1:

: head element


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e1 a2 b2

d2 b1

c2

d3

c1

d1

a1

d1 d2 d3 … b1

a2 b2

c1 c2

A

D B

C

D:Q1:

: head element

Subtree-matching

useless

blocked d1


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e1 a2 b2

d2 b1

c2

d3

c1

d1

a1

d1 d2 d3 … b1

a2 b2

c1 c2

A

D B

C

D:Q1:

: head element

Subtree-matching

useless

blocked d1,c1


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e1 a2 b2

d2 b1

c2

d3

c1

d1

a1

d1 d2 d3 … b1

a2 b2

c1 c2

A

D B

C

D:Q1:

: head element

Subtree-matching

-

useless -blocked d1,c1,a1,a2,b2,b1


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e1 a2 b2

d2 b1

c2

d3

c1

d1

a1

d1 d2 d3 … b1

a2 b2

c1 c2

A

D B

C

D:Q1:

: head element

Subtree-matching

-

useless -blocked d1,c1,a1,a2,b2,b1

A

D B

Q2:Subtree-matching

useless

blockedC


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Example: Classifying Head Elements (Tag+Level Streaming)

Subtree-matching

-

useless -blocked d1,c1, a1,a2,b2,b1

a1

e1 a2 b2

d2 b1

c2

d3

c1

d1

a1

d1 d2 d3 … b1

a2 b2

c1 c2

A

D B

C

D:Q1:

: head element

A

D B

C

Q2:Subtree-matching

d1

useless

blocked


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Subtree-matching

-


a1

e1 a2 b2

d2 b1

c2

d3

c1

d1

a1

d1 d2 d3 … b1

a2 b2

c1 c2

A

D B

C

D:Q1:

: head element

A

D B

C

Q2:Subtree-matching

d1

useless a1,b2blocked


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Subtree-matching

-


a1

e1 a2 b2

d2 b1

c2

d3

c1

d1

a1

d1 d2 d3 … b1

a2 b2

c1 c2

A

D B

C

D:Q1:

: head element

A

D B

C

Q2:Subtree-matching

d1

useless a1,b2blocked c1


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Subtree-matching

-


a1

e1 a2 b2

d2 b1

c2

d3

c1

d1

a1

d1 d2 d3 … b1

a2 b2

c1 c2

A

D B

C

D:Q1:

: head element

A

D B

C

Q2:Subtree-matching

d1

useless a1,b2blocked c1, b1, a2,


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Subtree-matching

-

useless -

blocked a1,a2,b1,b2,c1,d1

a1

e1 a2 b2

d2 b1

c2

d3

c1

d1

A

D B

C

Subtree-matching

d1,

useless a1,b2

blocked a2,b1,c1

A

D B

C

•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


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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.

a1

e1 a2 b2

d2 b1

c2

d3

c1

d1

A

D B

C

Q1:

Tag+Level Streaming


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a1

e1 a2 b2

d2 b1

c2

d3

c1

d1

A

D B

C

Q1:

Since all head elements are

blocked, we have to push a1 to stack and

output one path solution (a1,d1).

Tag+Level Streaming


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a1

e1 a2 b2

d2 b1 d3

c1

d1

A

D B

C

Q1:

If there is no c2, then (a1,d1) is a useless path solution.

Since all head elements are

blocked, we have to push a1 to stack and

output one path solution (a1,d1).

Tag+Level Streaming

c2


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iTwigJoin

Stream Manager

a1

c1 c2 c3 … b1

a2 b2

Temporary Storage

SA

SB SC

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.


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Flowchart of iTwigJoinLabel current head elements

as either subtree-Matching, Useless or Blocked

Discard Useless elements

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

If useless element is found

If not all streams end


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Optimal classes of iTwigJoin for three streaming schemes

A

B C

Tag Streaming A-D only pattern

Optimal classStreaming scheme

A-D only


33

A

B C

A

B C


Tag+Level Streaming A-D/P-C only pattern


A-D/P-C only

A-D only



34

A

B C

A

B C



Prefix Path Streaming


A-D/P-C only or 1-Branch node

A-D/P-C only

A-D only

A

B C

A-D/P-C only or 1-Branch



35

A

B C

A

B C



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

A

B C

More refined

Optimal class:Larger



36

Experiments

Benchmarks XMark: Synthetic Data Treebank: Real Data from Wall Street Journal


37

Experiments: I/O Performance

0

20000004000000

60000008000000

1000000012000000

14000000

Tree1 Tree2 Tree3 Tree4 Tree5

Ele

men

t Sca

nned

TwigStack TwigStackLst Tag+Level Prefix

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.


38

Experiments: Number of Intermediate PathsTree1: A-D only

Tree2: P-C only

Tree3: P-C only

Tree4: 1-branchnode

Tree5: 1-branchnode1

10

100

1000

10000

100000

Tree1 Tree2 Tree3 Tree4 Tree5In

term

ed

iate

Pa

ths

Ou

tpu

tTwigStack TwigStackLst Tag+Level Prefix

For treebank 5, there is no matching results. So Tag+Level and PPS do not output any intermediate results.


39

Experiments: Running Time

XMark1: Path Pattern,

XMark2: A-D only,

XMark3: P-C only,

XMark4: 1-branchnode,

XMark5: Non-optimal,

0

2

4

68

10

12

14

XMark1 XMark2 XMark3 XMark4 XMark5

Exe

cutio

n T

ime

(Sec

ond)

TwigStack TwigStackLst Tag+Level Prefix

Tag+level and PPS have better performance than TwigStack and TwigStackList in XMark data.


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.


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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.


42

END

Thank you! Q & A


43

Backup iTwigJoin AlgorithmWhile(not all streams end)

1. Label current head elements as either Matching, Useless or

Blocked

2. If any head element is Useless, discard it and continue

3. Let e1 be the matching element with the smallest startPos;

Let e2 be the blocked element with the smallest endPos;

4. If e2.endPos < e1.startPos, let e be the blocked element with

the smallest startPos; else let e be e1

5. Advance the stream e belongs to

6. Pop out elements from e’s stack whose endPos < e.startPos

7. Push e into its stack if e has a parent/ancestor in the

temporary storage system,

8. Output all paths involving e If the tag of e is a leaf node in Q

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