Structural Joins: A Primitive for Efficient XML Query Pattern Matching

1
Structural Joins A Primitive for Efficient XML
Query Pattern Matching

• Alkh02

2
Example XPath Query

• booktitleXML//author.jane
• Structural Relationships
• book/title, title/XML, book//author,
  author/jane

book
title
author
XML
jane
3
Overview

• Range-based XML Numbering Scheme
• (DocId, StartPosEndPos, LevelNum)
• Structural Relationships
• (D2, S2 E2, L2) is a descendant of (D1,S1
  E1,L1) iff D1D2, S1 lt S2 and E2 ltE1
• Parent-child above conditions L1 1 L2
• 2 Families of Structural Join Algorithms
• Tree-Merge Anc Desc
• Stack-Tree Anc Desc

4
A Sample XML Document Fragment Tree
Representation
5
Structural Join Algorithms

• AList a1, a2,
• list of potential ancestors, sorted on StartPos
• DList d1, d2,
• list of potential descendants, sorted on StartPos
• OutputList (ai,dj),
• join results, sorted
• Either by (DocId, ai.StartPos, dj.StartPos) //
  Anc version
• Or by (DocId, dj.StartPos, ai.StartPos) // Desc
  version

6
Algorithm Tree-Merge-Anc
7
Algorithm Tree-Merge-Desc
8
Stack-Tree Algorithms

• Depth first traversal of XML tree
• Conceptual merge of AList nodes DList nodes on
  StartPos
• Stack of AList nodes
• Node pushed onto the stack is a descendant of the
  node below it on the stack
• 3 cases (Stack-Tree-Desc version)
• A/DList node is not a descendant of stack top
  pop
• AList node is a descendant of stack top push
• D List node is a descendant of stack top output

9
Algorithm Stack-Tree-Desc (parent/child case)
a1 d1 a2 d2 . . . . an dn dn1 dn2
. . d2n
a1
d1
d2n
a2
an
d2
d2n-1
a3
. . .
...
d3
d2n-2
an
dn
dn1
a2
a1
? e.startPos gt stack-gttop.endPos

(a1,d1)
(a2,d2)
...
(an-1,dn-1)
(an,dn)
(an,dn1)
(an-1,dn2)
...
(a3,d2n-2)
(a2,d2n-1)
(a1,d2n)
10
Algorithm Stack-Tree-Desc
11
Algorithm Stack-Tree-Anc

• Problem
• Sorting on StartPos of DList nodes is
  natural/easy
• Sorting on StartPos of AList nodes is not
• Solution
• keep 2 lists of matching descendant nodes with
  each stack node
• self-list
• inherit-list

12
Algorithm Stack-Tree-Anc(parent/child case)
? e.startPos gt stack-gttop.endPos
a1 d1 a2 d2 . . . . an dn dn1 dn2
. . d2n
an
(an,dn)
(an,dn1)
. . .
(an-1,dn-1)
(an,dn), (an,dn1)
. . .
a2
(a2,d2)
(a2,d2n-1)
(a3,d3),(a3,d2n-2)...(an,dn),(an,dn1)
a1
(a1,d1)
(a1,d2n)
(a2,d2),(a2,d2n-1)...(an,dn),(an,dn1)
13
Algorithm Stack-Tree-Anc
14
Experiment XML Data Queries
15
Experimental Results
16
Efficient Structural Joins on Indexed XML
Documents

• Chie02

17
Motivation (Why using indices?)
18
A Sample XML Document
19
XML Data Indexed with B Tree

• Key (DocID, tag name, StartPos)

20
Algorithm Anc_Des_B
21
Typo

• Section 3. Structural Join using B-trees
  Chie02
• 4-th paragraph (i.e. 1-st paragraph of the right
  column of 4-th page)
• Correction
• Figure 3a depicts (2) pop a3 and a2 from the
  stack A list (4) push as follows after a2
  is popped from the stack, directly go to a14.
  Here than a2.end.
• ?
• Figure 3a depicts (2) pop a3 from the stack
  A list pop a2 (4) push as follows after a3 is
  popped from the stack, directly go to a14 (after
  popping up a2). Here than a2.end.
• Note
• The above paragraph is where how algorithm
  Stack_Tree_Desc Alkh 02 would work for the case
  of Fig. 3(a) is described. According to algorithm
  Stack_Tree_Desc Alkh 02, the corrected
  description is accurate.