Indexing and Querying XML Data for Regular Path Expressions

1
Indexing and Querying XML Data for Regular Path
Expressions

• Quanzhong Li and Bongki Moon
• Dept. of Computer Science
• University of Arizona
• VLDB 2001.

2
Querying XML

• XML has tree structured data model.
• Queries involve navigating data using regular
  path expressions.(e.g., XPath)
• e.g. /chapter/-/figure_at_captionTree Frogs
• Accessing all elements with same name string.
• Ancestor-descendant relationship between
  elements.

3
Contribution

• New system for Indexing XML data.
• Querying XML data based on a numbering scheme for
  elements
• Join algorithms for processing complex regular
  path expressions.

4
Outline

• Numbering scheme
• Index structure
• Join algorithms
• Experimental results

5
Path expression evaluation

• Previous approaches
• Conventional tree traversals
• Disadvantage Overhead of traversing for long or
  unknown path lengths.
• New approach
• Indexing for efficient element access.
• Numbering scheme for ancestor-descendant
  relationship.

6
Dietzs Numbering Scheme
(1,7)

• for two given nodes x and y, x is an ancestor of
  y, if and only if
• x occurs before y in the preorder traversal of T
  and
• after y in postorder traversal.

(6,6)
(2,4)
(7,5)
(3,1)
(5,3)
(4,2)
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Proposed numbering scheme

• This associates with each node
• a pair of numbers ltorder, sizegt
• as follows
• For a tree node y and its parent x,
• order(x) lt order(y)
• order(y)size(y) lt order(x) size(x)
• For two sibling nodes x and y, if x is the
  predecessor of y in preorder traversal then
• order(x) size(x) lt order(y)

(1,100)
(10,30)
(41,10)
(45,5)
(25,5)
(11,5)
(17,5)
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Advantages

• Efficient Updates
• Extra space can be reserved to accommodate future
  insertions.

9
Ancestordescendant relationship

• For two given nodes x and y of a tree T, x is an
  ancestor of y if and only if
• order(x) lt order(y) lt order(x) size(x).

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Outline

• Numbering scheme
• Index structure
• Join algorithms
• Experimental results

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Index and Data Organization
Query Processor
Query
Result
XISS
Element Index
Attribute Index
Structure Index
Name Index
Value Table
XML Raw Data
Document Loader
Paged File
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Element Index
Element nid
Element nid
Document ID list
B-tree
B-tree
ltOrder, Sizegt Depth, Parent ID
Element Record
Element list with the Same name in the Same
Document
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Structure Index
B-tree
Document ID (did)
nid, ltorder,sizegt, Parent order, Child
order, Sibling order, Attribute order
Array of All Elements And Attributes in the Same
Document
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Outline

• Numbering scheme
• Index structure
• Join algorithms
• Experimental results

15
Regular Path expression

• complex regular path expressions.
• e.g., /chapter/_/figure_at_captionTree Frogs

Symbol Function of symbol
__ Any single node
/ Union of node
Zero or more occurrences of a node
_at_ Denotes attributes
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Regular expression Decomposition

• A regular path expression can be decomposed to a
  combination of following basic subexpressions
• A subexpression with a single element or a single
  attribute,
• A subexpression with an element and an attribute
  ( e.g., figure_at_caption Tree Frogs)
• A subexpression with two elements (e.g.,
  chapter/figure or chapter/_/figure),
• A subexpression with a Kleene closure (,) of
  another subexpression, and
• A subexpression that is a union of two other
  subexpressions.

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Example

• ( E1 / E2 ) / E3 / ( ( E4 _at_A v ) ( E5 /
  _ / E6 ) )

E2
E3
E4
_at_Av
E5
E6
E1

/
/_/
EE-Join
EA-Join
EE-Join

/
KC-Join
Union
/
EE-Join
/
EE-Join
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Join algorithms

• Element Attribute join
• Element Element join
• Kleene Closure join

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EA-Join Algorithm

• Input
• E1..Em Ei is a set of elements having a common
  document identifier
• A1..An Aj is a set of attributes having a
  common document identifier
• Output
• A set of (e,a) pairs such that the element e is
  the parent of the attribute a.
• //Sort-merge Ei and Aj by document
  identifier.
• For each Ei and Aj with the same did do
• //Sort-merge Ei and Aj by PARENT-CHILD
  relationship.
• For each e in Ei and a in Aj do
• If ( e is a parent of a) then output (e,a)
• End
• End.

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Example
book
chapter
chapter
chapter
appendix
Figure
Figure
Figure
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Attribute-element position
chapter lt1,3gt
chapter lt1,3gt
chapterlt2,1gt
chapter lt3,1gt
name lt4,0gt
namelt2,0gt
name lt4,0gt
name lt3,0gt
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EE-Join Algorithm

• Input
• E1..Em and F1..Fn Ei and Fj is a set of
  elements having a common document identifier.
• Output
• A set of (e,f) pairs such that the element e is
  an ancestor of the element f.
• //Sort-merge Ei and Fj by doc. identifier.
• For each Ei and Fj with the same did do
• //Sort-merge Ei and Fj by ANCESTOR-DESCENDANT
  relationship.
• For each e in Ei and f in Fj do
• If (e is an ancestor of f ) then output (e,f)
• End
• End

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Extreme case of EE-Join
chapter lt1,90gt
chapter lt2,80gt
chapter lt8,20gt
chapter lt9,10gt
figure lt19,0gt
figure lt10,0gt
figure lt11,0gt
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KC-Join Algorithm

• Input
• E1..Em where Ei is a group of elements from an
  XML document.
• Output
• A Kleene Closure of E1..Em
• //Apply EE-Join algorithm repeatedly.
• Set x 1
• Set Ki E1..Em
• Repeat
• Set I I 1
• Set Ki EE-Join(Ei-1, E1)
• Until ( Ki is empty)
• Output union of K1,K2..Ki-1.

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Outline

• Numbering scheme
• Index structure
• Join algorithms
• Experimental results

26
Experiment Results

• Comparison with top-down and bottom-up evaluation
  methods.
• Comparison for
• EE-Join ( E1 /_/ E2 )
• EA-Join ( E_at_A )
• Scalability test

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EE-Join performance
28
EA-Join performance
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Results

• EE-Join algorithm outperformed bottom-up.
• EA-Join algorithm is comparable with top-down but
  outperformed bottom-up.
• Both are linearly scalable.