Bottom-up Evaluation of XPath Queries

1
Bottom-up Evaluation of XPath Queries

• Stephanie H. Li
• Zhiping Zou

2
Outline

• Overview of XPath
• Motivation
• Algorithms bottom-up evaluation
• Design and implementation

3
Introduction- Overview

• Overview of Xpath
• XPath is a querying language and is designed for
  addressing nodes of XML documents.
• Data model
• Syntax
• Expressions
• Location paths
• Operators
• Functions
• Evaluation(context)

4
Data Model

• Data Model
• XML document tree of nodes
• 7 kinds of nodes
• Element
• Attribute
• Text
• Namespace
• Processing-instruction
• Comment
• Document (root) nodes.

5
Data Model(Example)

• ltagt
• ltb/gt
• ltb/gt
• ltb/gt
• ltb/gt
• lt/agt

6
Expression

• XPath uses expressions to select nodes from XML
  documents
• The main types of expressions are
• Location Paths, Functions and operators

7
Location Paths

• Although there are many different kinds of XPath
  expressions, the one thats of primary use in
  Java programs is the location path.
• Location Path
• /childmovies/childmovieposition()5
• step axis nodetest predicate
• location path

8
Location Step

• AxisNodetestpredicts
• Axis chooses the direction to move from the
  context node
• Node test determines what kinds of nodes will be
  selected along that axis
• Predicts further filter the node-set.

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XPath Axis

• Axis---main navigator for a XML doc
• ancestor nodes along the path
  to the root
• ancestor-or-self same but including the
  context node
• child children of the
  context node
• descendant descendants of the
  context node
• descendant-or-self same but including the
  context node
• following nodes after the
  context node in document order,
  excluding descendants
• following-sibling following sibling of the
  context node
• parent the parent of the
  context node
• preceding nodes before the
  context node in document
  
  order,excluding ancestors
• preceding-sibling preceding sibling of the
  context node

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Node Test

• Node Type test
• Example
• T(root()) r,
• T(element()) a b1 b4
• T(element(a)) a
• T(element(b)) b1 b4
• Node Name test
• Element node name

11
Operators and Functions

• Arithmetic Ops
• Ops for comparisons and boolean logic
• lt,gt,lt,gt,,! or, and
• Functions
• Position()
• Last()

12
Xpath Query Evalutation

• Query evaluation is a major algorithmic problem
• Main construct is the expression
• Each expression is evaluated to yield an object
  one of these four types
• Node-set (an unordered collection of nodes
  without duplicates )
• Boolean(true or false)
• Number(a floating-point number )
• String

13
Context

• All XPath expressions are evaluated w.r.t. a
  Context,which consists of
• A context node
• A context position(int)
• A context size(int)
• The input context for query evaluation is chosen
  by the user.

14
Motivation

• Claim
• The way XPath is defined in W3C XPath
  recommendation motivates an inefficient
  implementation (exponential-time).
• This paper propose more efficient way
  (polynomial-time)

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Basic query evaluation strategy

• 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.first to node n0
• if (Q.tail is not empty) then
• for each node n ? S do
• process-location-step(n, Q.tail)
• End
• Time(Q) D Time(Q-1) or DQ when
  Q gt 0
• 1 when Q
  0

The algorithm recursively evaluates each
remaining step for each matching node of the
current step
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Xpath Evaluate in PTime

• Theorem Let e be an arbitrary XPath expression.
  Then, for context node x, position k, and size n,
  the value of e is v, where v is the unique value
  such that ltx,k,n,vgt? E?e
• The main principle that the paper propose to
  obtain an XPath evaluation algorithm with PTime
  complexity is the notion of a context-value
  table(CVT)

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Context-value table Principle

• Given an expression e, the CVT of e specifies all
  valid combinations of contexts cltx,k,ngt and
  values v, s.t. e evaluates to v in context
  cltx,k,ngt
• Such a table for expression e is obtained by
  first computing the CVTs of the direct
  subexpressions of e and then combining them into
  the CVT for e.
• The size of each of the CVTs has a polynomial
  bound
• Each of the combination steps can be effected in
  PTime
• Thus, query evaluation in total under our
  principle also has a PTime bound

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Bottom-up evaluation of XPath
19
Bottom-up evaluation of XPath

• Algorithm (Bottom-up algorithm for XPath)
• Input An XPath query Q
• Output E?Q
• Method
• Let Tree(Q) be the parse tree of query Q
• RØ
• For each atomic expression l ? leaves(Tree(Q)) do
• compute table E?l and add it to R Note
  we use JDom to do this
• While E?root(Tree(Q))! ? R do
• Begin
• take an Op(l1,ln) nodes(Tree(Q))
• s.t. E?l1, E?ln ? R
• compute E?Op(l1,ln) using E?l1,, E?ln
• add E?Op(l1,ln) to R
• End
• Return E?root(Tree(Q))

By a bottom-up algorithm we mean a method of
processing XPath while traversing the parse tree
of the query from its leaves up to its root.
20
Bottom-up evaluation of XPath

• Example
• XML

lt?xml version"1.0"?gt ltpeoplegt ltperson
born"1912" died"1954" id"p342"gt ltnamegt
Alan Turing lt/namegt lt!-- Did the word
computer scientist exist in Turing's day? --gt
ltprofessiongtcomputer scientistlt/professiongt
ltprofessiongtmathematicianlt/professiongt
ltprofessiongtcryptographerlt/professiongt
lthomepagegthref"http//www.turing.org.uk/"lt/homepa
gegt lt/persongt ltperson born"1918"
died"1988" id"p4567"gt ltnamegtRichard M.
Feynmanlt/namegt ltprofessiongtphysicistlt/profes
siongt lthobbygtPlaying the bongoeslt/hobbygt
lt/persongt lt/peoplegt
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Example XML Doc Tree
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Example XPath Query tree

• Parse tree XPath query
• descendant profession/following-siblingposit
  ion()! last()

23
Example Evaluate subexpressions
24
Example Evaluate subexpressions
25
Example Evaluate subexpressions
26
Design and Implementaion

• Environment
• Java,JDK1.5.0
• Jdom1.0
• XPath1.0
• Features
• Only Element nodes are queried
• Not support abbreviated xpath expressions
• Not support format of location steps in predicts.

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System Structure
User input (MyDriver.java)
XML file Query Context node
Query Parser (Parser.java BinaryTree.java,Node.jav
a)
JDom XML parser (org.jdom.input.SAXBuilder)
Query tree
XML document tree
Evaluator( QueryEval.java)
Context value tables (ContextValTable.java and
others)
Result for the full xpath query
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Conclusion

• XPath query evaluation algorithm that runs in
  polynomial time with respect to the size of both
  the data and the query (linear in the size of
  queries and quadratic in the size of data)
• No optimization, strictly coheres to the
  specification given in the paper

29
References

• G. Gottlob, C. Koch, and R. Pichler. "Xpath
  Processing in a Nutshell". In Proceedings of the
  19th IEEE International Conference on Data
  Engineering (ICDE'03), Bangalore, India, Mar.
  2003.
• G. Gottlob, C. Koch, and R. Pichler. "Efficient
  Algorithms for Processing XPath Queries". In
  Proceedings of the 28th International Conference
  on Very Large Data Bases (VLDB'02), Hong Kong,
  China, Aug. 2002.
• G. Gottlob, C. Koch, and R. Pichler. "XPath Query
  Evaluation Improving Time and Space Efficiency".
  In Proceedings of the 19th IEEE International
  Conference on Data Engineering (ICDE'03),
  Bangalore, India, Mar. 2003.
• http//www.ibiblio.org/xml/books/xmljava/chapters/
  ch16.html