Holistic Twig Joins: Optimal XML Pattern Matching

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Holistic Twig Joins Optimal XML Pattern Matching

• Author Nicolas Bruno
• Nick Koudas
• Divesh Srivastava
• Presented by Huang Yukai

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Outline

• 1. Background
• 2. Algorithm PathStack
• 3. Algorithm TwigStack
• 4. Experiments
• 5. Conclusion References

3
Background (1)

• An XML database is a forest of rooted, ordered,
  labeled trees, each node corresponding to an
  element or a value, and the edges representing
  the relationships.

ltbookgt lttitlegt XML lt/titlegt ltall
authorsgt ltauthorgt ltfngt jane lt/fngt ltlngt poe
lt/fngt ltauthorgt ...... lt/all authorsgt ltyeargt
2000 lt/yeargt ...... lt/bookgt
book
title
all authors
year
...
XML
author
2000
...
fn
ln
jane
poe
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Background (2)

• XML queries specify patterns of selection
  predicates on multiple elements.
• e.g. booktitle xml//authorfn jane AND
  ln poe

book

• Finding all occurrences of such a twig pattern in
  an XML database is a core operation for XML query
  processing.

title
author
fn
ln
xml
jane
poe
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Background (3)

• The previous work
• (i) decompose the twig pattern into binary
  structural relationships.
• (ii) match the binary relationships against the
  XML database.
• (iii) stitch together these basic matches.

book

• Drawbacks
• the intermediate result size can get too large!

title
author
fn
ln
motivation algorithm complexity should be
independent of the size of intermediate results
xml
jane
poe
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Background (4)

• Labeling method

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Outline

• 1. Background
• 2. Algorithm PathStack
• 3. Algorithm TwigStack
• 4. Experiments
• 5. Conclusion References

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PathStack (1)

• Notation
• q denote twig patterns (and the root node of
  twig pattern)
• Associated with each node q in query twig pattern
  there is a stream Tq contains all the positional
  representations of node q in database and sorted
  by (DocId, LeftPos).
• Associated with each q there is a stack Sq
  contains the pairs (positional representation in
  Tq, point to a node in Sparent(q))

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PathStack (2.1) an example

• Input data D and query Q

• position representations of each nodes in data

A1
B1
A1 (1,19,1) B1 (1,28,2) A1 (1,37,3) B1
(1,46,4) C1 (1,55,5)
A
A2
B
B2
C
C1
Q
D
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PathStack (2.2) an example

• Phase 1 construct stacks

(1) For each node in q, we get stream Tq from XML
database
Ta A1, A2 (eof) Tb B1, B2 (eof) Tc C1 (eof)
(2) loop while eof(Tq) is false, where q is leaf
node.


Push stack
A1
B1
A2
C1
B2
A2
B2
C1
A1
B1
Sc
SB
SA
node C is leaf node and Tc is eof.
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PathStack (2.3) an example

• Phase 2 output all the solutions with the stacks

A2
B2
C1
A1
B1
Sc
SB
SA
Query results A1B1C1 A1B2C1 A2B2C1
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PathStack (3)

• Algorithm PathStack

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PathStack (4)

• Procedure showSolutions

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Outline

• 1. Background
• 2. Algorithm PathStack
• 3. Algorithm TwigStack
• 4. Experiments
• 5. Conclusion References

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TwigStack (1)

• A straightforward way is to decompose the twig
  into multiple path patterns, use PathStack to get
  partial solutions and merge them finally.
• Drawback!

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TwigStack (2) an example

• Input data D and query Q

R
A
A1
A2
B
C
B1
C1
B2
C2
D
F
D1
E
D2
F

• How to skip node A1?

D
Q
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XB-trees

• XB-tree a variant B-tree for indexing the
  positional representation (DocId, LeftPos
  RightPos, LevelNum) of elements in XML tree.
• The nodes in page are sorted by DocId and
  LeftPos.
• The node in internal page contains bounding
  segment N.L, N.R, all its child nodes included
  in the segment.
• Two operations over XB-trees Advance Drilldown
• TwigStackXB (omitted)

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Outline

• 1. Background
• 2. Algorithm PathStack
• 3. Algorithm TwigStack
• 4. Experiments
• 5. Conclusion References

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Experiments (1)

• Experimental Setting
• Implemented in C
• A computer with 550Mhz Pentium III processor,
  768MB of main memory and a 2GB disk.
• Datasets
• (a) synthetic data random generated trees with
  parameters depth, fan-out and labels.
• (b) real-world data an unfolded fragment of
  the DBLP database.

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Experiments (2)

• PathStack vs. Binary Structural Joins

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Experiments (3.1)

• PathStack vs. PathMPMJ3

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Experiments (3.2)

• PathStack vs. PathMPMJ3

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Experiments (4)

• PathStack vs. TwigStack
• Queries

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Experiments (5)

• Using XB-trees

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Conclusions

• Holistic join algorithms PathStack and
  TwigStack.
• More issues
• to handle more complicated XPath expressions.
• value-based joins (e.g. links across documents)

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References

• 1 N. Bruno, N. Koudas, D. Srivastava. Holistic
  Twig Joins Optimal XML Pattern Matching.
  Technical Report. ...
• 2 S.Al-Khalifa, H. V. Jagadish, N. Koudas, J.
  M. Patel, D.Srivastava, and Y. Wu. Structural
  joins A primitive for efficient XML query
  pattern matching. ICDE 02. some stack-based
  algorithms for joins
• 3 C. Zhang, J. Naughton, D. Dewitt, Q. Luo, and
  G. Lohman. On supporting containment queries in
  relational database management systems. SIGMOD
  01. the MPMGJN algorithm