XPath Query Evaluation - A Top Down Approach

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XPath Query Evaluation- A Top Down Approach

• Mohammed Pithapurwala (mp66_at_cse.buffalo.edu)
• Pejus Das (pejusdas_at_cse.buffalo.edu)

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Introduction

• XPath Query Evaluation
• Uses
• Select nodes in XML document
• XSLT, XQuery
• Polynomial V/s Exponential
• Top Down Algorithm

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XPath

• What is XPath?
• childsectionposition()lt6 / descendantcite /
  attributehref
• selects all href attributes in cite elements in
  the first 5 sections of an article document
• Structure of XPath expression
• Axes
• Node types
• Node test
• Returns
• Number, node set, string, boolean

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Implementation

• XPath Axes
• Child
• Parent
• Descendant
• Axes Functions
• FirstChild
• nextSibling
• Child firstchild.nextsibling
• Parent (nextsibling-1).firstchild-1
• Descendant firstchild.(firstchild ??
  nextsibling)

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Code Snippet

• public static Element firstChild(Element
  currNode)
• Element fChild
• fChild null
• List childNode currNode.getChildren()
• Iterator iterator childNode.iterator()
• if(iterator.hasNext())
• fChild (Element) iterator.next()
• return(fChild)

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Node Test Expressions

• Node Test Expression
• T(node()) all nodes in the document
• T(attribute(href)) all nodes labelled href
• attribute(S) child(S)?? T(attribute())
• Node Numbering
• lt doc, X
• The node order relative to the axes X in document
  order
• idxx(x,S)
• Context
• c ?x, k, n?
• x node
• k position of the node
• n context size
• Evaluation of XPath relative to context

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XPath Evaluation

• Xte
• X ? child, parent, descendant, .
• t node test expression
• e expression
• Expressions
• e ? node set, number, string, boolean
• ArithOp ? , -, , div, mod
• EqOP ? ?, ?

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XPath Semantics
????x, k, n? P???(x) ?position()? (?x, k, n?)
k ?last()? (?x, k, n?) n For all other
kinds of expressions, e Op(e1, , em) ?Op(e1,
, em)?(c) ???Op?(?e1?(c),.,?em?(c)) maps a
context to a value type.
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Intuitive Algorithm
P ?t?e1? ?em? (x) begin S
y x ? y, y ? T(t) for 1 ? i ? m
(in ascending order) do S y ?
S ??ei? (y, idx?(y,S), S true
return S end P??1?2?(x) P??1?(x)
P??2?(x) P?/?? (x) P???(root) P??1/?2?(x)
Uy ? P?1(x)P??2?(y)
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Runtime

• Ex
• Doc ltagtltb/gtltb/gtlt/agt
• Query //a/b/parenta/b/parenta/b
• Construct more queries /parenta/b
• procedure process-location-step(n0, Q)
• / n0 is the context node query Q is a list of
  location steps /
• begin
• node set S apply Q.head to node n0
• if (Q.tail is not empty) then
• for each node n 2 S do process-location-step(n,
  Q.tail)
• End
• Complexity Time(Q) DQ

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Algorithm

• S???te1em?(X1, ,Xk)
• begin
• S ??x,y? x?? Xi , x ? y, and y??
  T(t)
• for each 1 i m (in ascending order) do
• begin
• Fix some order S ??x1,y1 ?, , ?xl,yl?? for S
• ?r1,rl? ?ei?(t1,,tl)
• where tj ? yj , idx? (yj,, Sj ), Sj ?
• and Sj z ? xj, z ? ? S
• S ?xi,yi? ri is true
• end
• for each 1 i k do
• Ri y ? x, y ? ? S, x ? Xi
• return ?R1, ,Rk ?
• end

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Algorithm (contd.)
S??/??(X1, ., Xk) S????(root, ., k
times) S???1/?2?(X1, ., Xk)
S???2?(S???1?(X1, ., Xk)) S???1?2?(X1, .,
Xk) S???1?(X1, ., Xk) U??
(S???2?(X1, ., Xk))
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Semantics Function
?????(?x1, k1, n1?, , ?xl, kl, nl?)
S????(x1, ., xl) ???position()?(?x1, k1,
n1?, , ?xl, kl, nl?) ?k1, ., kl?
???last()?(?x1, k1, n1?, , ?xl, kl, nl?)
?n1, ., nl? And ???Op(e1, . em?(c1, ., cl)
??Op? ?? (???e1?(c1, ., cl), .,
???em?(c1, ., cl)) For remaining kind of
expressions
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Benchmark Results in seconds for IE6 vs. the
implementation
Q IE6 IE6 IE6 Top Down Algorithm Top Down Algorithm Top Down Algorithm Top Down Algorithm Top Down Algorithm
Q 10 20 200 10 20 200 500 1000
1 0.00 0.00 0.00 0.00 0.00
2 2 0.00 0.00 0.02 0.12 0.57
3 346 0.00 0.00 0.02 0.23 1.14
4 1 0.00 0.00 0.05 0.33 1.70
5 21 0.00 0.00 0.07 0.44 2.32
6 5 406 0.00 0.00 0.09 0.54 2.88
7 42 0.00 0.00 0.12 0.67 3.45
8 437 0.00 0.00 0.14 0.78 4.03
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References

• G. Gottlob, Ch. Koch, R. Pichler XPath
  Processing in a Nutshell. SIGMOD Record,
  March'03.
• G. Gottlob, Ch. Koch, R. Pichler Efficient
  Algorithms for Processing XPath Queries. ACM
  TODS, to appear.

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• ?

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• Thank You!!