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Efficient Processing of XML Twig Patterns with Parent Child Edges: A Look-ahead Approach
Jiaheng Lu, Ting Chen, Tok Wang Ling
National University of Singapore
Nov. 11. 2004
CIKM 2004 Washington D.C. U.S.A.
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Outline
☞☞ XML Twig Pattern Matching Problem definition State of the Art: TwigStack Sub-optimality of TwigStack
Our algorithm: TwigStackList Performance Conclusion
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XML Twig Pattern Matching An XML document is commonly modeled as a rooted,
ordered and labeled tree.
book
preface chapter chapter
section
section
figure
paragraph
section
figure
paragraph figure
paragraph
………….
title
title
“XML”“Data”
“Intro”
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Regional Coding Node Label1: (startPos: endPos, LevelNum) E.g.
book (0: 32, 1)
preface (1:3, 2) chapter (4:29, 2) chapter(30:31, 2)
“Intro” (2:2, 3) section (5:28, 3)
section(9:17, 4)
figure (14:15, 6)
paragraph(13:16, 5)
section(18:23, 4)
figure (20:21, 6)
paragraph(19:22, 5)figure (25:26, 5)
paragraph(24:27, 4)title: (6:8, 4)
title: (10:12, 5)
1. M.P. Consens and T.Milo. Optimizing queries on files. In In Proceedings of ACM SIGMOD, 1994.
“Data” (7:7, 3)
“XML” (11:11, 3)
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What is a Twig Pattern? A twig pattern is a small tree whose nodes are tags, attributes or
text values and edges are either Parent-Child (P-C) edges or
Ancestor-Descendant (A-D) edges. E.g. Selects Figure elements which are descendants of Paragraph
elements which in turn are children of Section elements having child element Title
Twig pattern :
Section
Title Paragraph
Figure
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XML Twig Pattern Matching
Problem Statement Given a query twig pattern Q, and an XML database
D, we need to compute ALL the answers to Q in D. E.g. Consider Q1 and Doc 1:
Doc1:
s1
s2
f1
p1
t1
t2
Section
title figure
Query solutions: (s1, t1, f1) (s2, t2, f1) (s1, t2, f1)
Q1:
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Previous work: TwigStack TwigStack2: a holistic approach
Two-phase algorithm: Phase 1 TwigJoin: intermediate root-leaf paths are outputted Phase 2 Merge: merge the intermediate path list to get the result
2. N. Bruno, D. Srivastava, and N. Koudas. Holistic twig joins: optimal xml pattern matching. In In Proceedings of ACM SIGMOD, 2002.
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Previous work: TwigStack
A node q in a twig pattern Q is associated with a stack Sq
Insertion and deletion in a stack Sq
Insertion: An element eq from stream Tq is pushed into its stack Sq if and only if
eq has a descendant eqi in each Tqi , where qi is a child of q
Each node eqi recursively has the first property
Deletion: An element eq is popped out from its stack if all matches involving it have been output.
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Sub-optimality of TwigStack
TwigStack is I/O optimal for only ancestor-descendant edge query
Unfortunately, TwigStack is sub-optimal for queries with any parent-child edge.
TwigStack may output a large size of intermediate results that are not merge-joinable to any final solution for queries with parent-child relationships.
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Sub-optimality of TwigStack: an example
Twig Patterns1
p1
f1
t2
t1
Section
title paragraph
figure
A simple XML tree
Since s1 has descendants t1,p1 and in turn p1 has descendant f1, TwigStack output an intermediate path solution <s1,t1>.
But it is useless, for there is no solution for this example at all.
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Main problem and our experiment
TwigStack might output some intermediate results that are useless to query answers .
To have a better understanding , we perform TwigStack on real dataset.
Data set : TreeBank[from U. of Washington XML datasets] Queries:
Q1:VP [/DT] //PRP_DOLLAR_ Q2: S//NP[//PP/TO][/VP/_NONE_]/JJ Q3: S [/JJ] /NP
All queries contain parent-child relationships.
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Our experimental results
Intermediate paths by TwigStack
Merge-joinable paths
Percentage of useless intermediate paths
Q1 10,663 5 99.9%
Q2 24,493 49 99.5%
Q3 70,967 10 99.9%
Most intermediate paths do not contribute to final answers due to parent-child edges!
It is a big challenge to improve TwigStack to answer queries with parent-child edges.
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Intuition for improvement
Twig Patterns1
p1
f1
t2
t1
Section
title paragraph
figure
A simple XML tree
Our intuitive observation: why not read more paragraph elements and cache them in the main memory?
For example, after we scan the p1, we do not stop and continue to read the next paragraph element. Then we find that there is only one paragraph element and f1 is not the child of paragraph. So we should not output any intermediate solution.
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Outline
XML Twig Pattern Matching Problem definition State of the Art: TwigStack Sub-optimality of TwigStack
☞☞ Our algorithm TwigStackList Experimental results Conclusion
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Our main idea
Main idea: we read more elements in the input streams and cache some of them in the main memory so that we can make a more accurate decision about whether an element can contribute to final answer.
But we cannot cache too many elements in the main memory. For each node q in twig query, the number of elements with tag q cached in the main memory should not be greater than the longest path in the XML dataset.
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Our caching method What elements should be cached into the main memory?
Only those that might contribute to final answers
s1
p1
p3p2
t1
A simple XML tree
f1
We only need to cache p1,p3 into main memory, why not p2? Because if p2 contributed to final answers, then there would be an element before f1 to become the child
of p2. But now we see that f1 is the first element. So p2 is guaranteed not to contribute to final answers.
Twig Pattern
Section
title paragraph
figure
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Our criteria for pushing an element to stack
The criteria for an element to be pushed into stack is very important for controlling intermediate results. Why?
Because, once an element is pushed into stack, then this element is ready to output. So less elements are pushed into stack, less intermediate results are output.
Our criteria: Given an element eq from stream Tq, before eq is pushed into stack Sq , we ensure that
(i) element eq has a descendant eq’ for each child q’ of q, and (ii) if (q, q’) is a parent-child relationship, eq’ has parent with tag q i
n the path from eq to eqmax , where eqmax is the descendant of eq with the maximal start value, qmax being a child of q.
(iii) each of q’ recursively satisfy the first two conditions.
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Examples
s1
p1
p3p2
t1
A simple XML tree
f1 Element p3 can be pushed into stack , but p1, p2 cannot. Because p3 has a child f1. Although p1 has a descendant f1, but f1 is not the child of p1.
Twig PatternSection
title paragraph
figure
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Our algorithm: TwigStackList We propose a novel holistic twig algorithm TwigSt
acklist to evaluate a twig query. Unique features of TwigStackList:
It considers the parent-child edge in the query There is a list for each query node to cache elements th
at likely participate in final solutions. It identifies a broader class of optimal queries. TwigSta
ckList can guarantee the I/O optimality for queries with only ancestor-descendant edges connecting branching nodes and their children.
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TwigStackList : an exampleTwig Pattern
Section
title paragraph
figure
An XML tree
Stack List
s1
p1
p3
f1
t1
t2
s2
p2t3
f2
Root
p2
s2
t3
f2
p3p3 p1
Scan s1, t1, p1 ,f1.
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TwigStackList : an exampleTwig Pattern
Section
title paragraph
figure
An XML tree
Stack List
s1
p1
p3
f1
t1
t2
s2
p2t3
f2
Root
p2
s2
t3
f2
p3p3 p1
Since p1 is not the parent of f1 (but ancestor) , we continue to scan p2 and put p1 to list.
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TwigStackList : an exampleTwig Pattern
Section
title paragraph
figure
An XML tree
Stack List
s1
p1
p3
f1
t1
t2
s2
p2t3
f2
Root
p2
s2
t3
f2
p3p3 p1
Put p2,p3 to list and the cursor points to p3, for it is the parent of f2.
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TwigStackList : an exampleTwig Pattern
Section
title paragraph
figure
An XML tree
Stack List
s1
p1
p3
f1
t1
t2
s2
p2t3
f2
Root
p2
s2
t3
Output intermediate solutions: <s2,t3>
f2
,<s2,p3,f2> Final: <s2,t3,p3,f2>Merge
p3p3 p1
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TwigStackList v.s. TwigStack
TwigStackList shows I/O optimal for the above query. In contrast, TwigStack shows sub-optimal, for it output the “uesless” path solution < s1,t1>
Twig Pattern
s1
p1
Section
titleparagraph
figure
p3
f1
t1
An XML tree
t2
s2
p2t3
f2
Root
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Sub-optimality of TwigStackList Although TwigStackList broadens the class of optimal query compared to TwigSt
ack, TwigStackList is still show sub-optimality for queries with parent-child edge connecting branching nodes.
Twig Pattern
s1
s2
p1
t1
Section
title paragraph
A simple XML tree
Observe that there is no matching solution for this dataset. But TwigStackList caches s1 and s2 in the list and push s1 to stack. So (s1,t1) will be output as a useless solution.
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Sub-optimality of TwigStackList Although TwigStackList broadens the class of optimal query compared to TwigSt
ack, TwigStackList is still show sub-optimality for queries with parent-child edge connecting branching nodes.
Twig Pattern
s1
s2
p1
t1
Section
title paragraph
A simple XML tree
Observe that there is no matching solution for this dataset. But TwigStackList caches s1 and s2 in the list and push s1 to stack. So (s1,t1) will be output as a useless solution.
p2
Here the behavior of TwigStackList is still reasonable since we do not know whether s1 has a child p2 following p1 before we advance p1.
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Outline
XML Twig Pattern Matching Problem definition State of the Art: TwigStack Sub-optimality of TwigStack
Our algorithm TwigStackList ☞☞ Experimental results Conclusion
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Experimental Setting
Experimental Setting Pentium 4 CPU, RAM 768MB, disk 2GB TreeBank
Download from University of Washington XML dataset Maximal depth 36, 2.4 million nodes
Random Seven tags : a, b, c, d, e, f, g. ; uniform distributed Fan-out of elements varied 2-100, depth varied 10-100
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Performance against TreeBank
Queries with XPath expression:
Number of intermediate path solutions for TwigStackList V.s. TwigStack
TwigStack TwigStackList Reduction percentage Useful Path
Q1 35 35 0% 35
Q2 2957 143 95% 92
Q3 25892 4612 82% 4612
Q4 10663 11 99.9% 5
Q5 702391 22565 96.8% 22565
Q6 70988 30 99.9% 10
Q1 S[//MD]//ADJ Q4 VP[/DT]//PRP_DOLLAR_
Q2 S/VP/PP[/NP/VBN]/IN Q5 S[//VP/IN]//NP
Q3 S/VP//PP[//NP/VBN]//IN Q6 S[/JJ]/NP
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Performance analysis We have three observations: (1) when queries contain only ancestor-descendant ed
ges, two algorithms have similar performance. See Q1. (2)When edges connecting branching nodes contain o
nly ancestor-descendant relationships, TwigStack is optimal, but TwigStack show the sub-optimal. See Q3.Q5
(3) When edges connecting branching nodes contain parent-child relationships, both TwigStack and TwigStackList are sub-optimal. But TwigStack typically output far few “useless” (<5%) intermediate solution than TwigStack. See Q2,Q4,Q6.
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Performance against random dataset
(a ) Q 1 (b ) Q 2 (c) Q 3
(d ) Q 4 (e) Q 5
a
b c
d e f g
a
aa
a
bb
bb cc
d
e
f
g
d
e
f
g
c d
e f g
c d
e f g
TwigStack TwigStackList Reduction Useful Path
Q1 9048 4354 52% 2077
Q2 1098 467 57% 100
Q3 25901 14476 44% 14476
Q4 32875 16775 49% 16775
Q5 3896 1320 66% 566
From the following table, we see that for all queries, TwigStackList again is more efficient than TwigStack in terms of the size of intermediate results.
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Outline
XML Twig Pattern Matching Problem definition State of the Art: TwigStack Sub-optimality of TwigStack
Our algorithm TwigStackList Experimental results ☞☞ Conclusion
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Conclusion Previous algorithm TwigStack show the sub-optimality f
or queries with parent-child edges. We propose a new algorithm TwigStackList to address t
his problem. TwigStackList broadens the class of query with I/O opti
mality. Experiments show that TwigStackList typically output m
uch fewer useless intermediate result as far as the query contains parent-child edges.
We recommend to use TwigStackList as a new holistic join algorithm to evaluate a query with parent-child edges.
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Thank You! Q & A
