1. Indexing Methods for Efficient XML Query Processing
Jun-Ki Min

2. XML eXtensible Markup Language The de facto standard XML Data
data representation and exchange on the Web
XML Data
An instance of semistructured data
self-describing
irregularly structured

3. XML Data Comprise hierarchically nested collections of elements
Element can contains
Atomic data value
A sequences of subelements
attributes composed of name-value pairs
ID-IDREF relationship
Tree or Graph representation

4. XML Example 1 6 2 3 book title paper libraryDB 7 editor author 4 10 9
<book editor = 1>
<title> title1 </title>
<author> author1 </author>
<chapter> … </chapter>
</book>
<paper>
<title> title2</title>
<author id = 1> author2 </author>
<author> author3 </author>
<section> … </section>
</paper> …
</libraryDB> 1 6 2 3
book
title
paper
libraryDB 7
editor
author 4 10 9
section 8 5
chapter
Index Fabric
ToXin
APEX

5. XML Query XML Query Language Structural Summary & Path Index
XSLT, XML-QL, XPath, XQuery
use path expression to traverse the irregularly structured data
ex) /libraryDB/book/title or //title
search the whole XML data => inefficiency
Structural Summary & Path Index
by restricting the search to only relevant portions of XML Data

6. Schemas for XML DTD, XML Schema Structural Summary Path Index
Specifies the constraints of XML Data
<!ELEMENT book (title, author+,chapter*)>
are not mandatory
=> lack of external schema
Structural Summary
Summary of label paths
Path Index
Structural Summary + Extents

7. Schemas for XML Applications User Interface Query Formulation
XML Data Design, Editing
Query Formulation
Query Validation
Query Optimization
Path Index

8. Structural Summary DTD Extraction Structural Summary XTRACT
based on element information
Structural Summary
Representative Objects
based on path information

9. XTRACT [Garofalakis, Gionis, Rastogi, Seshadri, Shim: SIGMOD 00]
Infer concise and accurate DTD
Choose a DTD from candidate DTDs
(a b),(b a) => (a|b)* or (a b)|(b a)
Based on Minimum Description Length (MDL) Principle
ranks each candidate DTDs depending on the number of bits required to describe the subelement sequences in terms of the candidate DTD
6(for DTD)+3+3 = 12
9(for DTD)+1+1 = 11

10. Representative Objects(RO)
[Nestorov, Ullman, Wiener, Chawathe : ICDE 97]
Provide a concise representation of the inherent schema of a semistructured hierarchical data
Full-RO
Describe all simple paths
K-RO
K-RO guarantees that its paths whose length are k+1 exist in data.
1-RO
Simplest & very compacted representation

11. Representative Objects(RO)
book
title
paper
libraryDB
editor
author
section
chapter
Graph Representation of 1-RO
name
book
title
paper
libraryDB
editor
author
section
chapter
XML Data
name
book
title
paper
libraryDB
editor
author
section
chapter
Graph Representation of 2-RO(= Full-RO)
name

12. Path Index Access Support Relations Deterministic Non-Deterministic
Strong DataGuide
Index Fabric
ToXin
APEX
Non-Deterministic
1-Index
A(k) Index
F&B Index

13. Access Support Relations
[Kemper, Moerkotte: IS 92]
Originated from OODBMS
select Name
from Mercedes.Manufactures.Composition.Division
To support join along arbitrary reference chains
Generalization of Join Index[Valduriez 87]
Based on the paths in the schema
Materialize access paths of arbitrary length
Support only predefined subsets of paths.

14. DataGuides [Goldman, Widom : VLDB 97]
An implementation version of Full-RO
Summary of label paths from the root (= simple paths)
Concise: describe every unique simple path exactly once, regardless of the number of times it appears
Accuracy: do not contains label paths that do not appear in the data
Convenience: can store and access it using similar techniques available for processing semistructured data

15. DataGuides
Construction Algorithm emulates the conversion algorithm from non-deterministic finite automata (NFA) to deterministic finite automata (DFA)
Intuitively, a simple path is represented as a node in DataGuide
One XML Data may have multiple DataGuides A B C
An XML Data A B C
Various DataGuides

16. Strong DataGuide
If the sets of nodes which are reachable for simple paths are equal, then the simple paths are represented as a single node.
Linear time and linear space for tree structured data
Exponential time and exponential space for graph structured data 1 A C B 2 3 4 5 6
2,4
3,5
Source Strong DataGuide Source Strong DataGuide

17. 1/2/T-Index [Milo and Suciu: ICDT 99] 1-Index
Summary all label paths starting from the root
Support queries of q= Px where P = /l1/l2/…/ln
Non-deterministic
Based on backward bisimulation which is originated from graph verification
Extents are disjoint
More compact size than Strong DataGuides

18. 1-Index Equivalence relation (≡) Backward Bisimulation (≈b)
v ≡ u iff Lv =Lu
where Lx = {w| w is a simple path from the root to x}
the collection of all equivalence class
Exponential construction cost
Backward Bisimulation (≈b)
If x≈by and x is the root then y is the root
Conversely, If x≈by and y is the root, then x is the root.
If x≈by and <x’l x> is an edge, then there is exists an edge (y’l y), such that x’ ≈by’
Conversely, if x≈by and (y’l y) is an edge, then there exists an edge (x’l x) such that x’≈by’

19. ≡ vs ≈b ≈b X ≡ Y since LX = LY = {a.b.d, a.c.d} X Y v ≈b u  v ≡ u
O(mlogm) construction cost [Paige and Tarjan 87] ≈b

20. 1-Index vs Strong DataGuide6 2 3
book
title
paper
libraryDB 7
editor
author 10
8,9
section 8 5
chapter
Strong DataGuide 4 1 6 2 3
book
title
paper
libraryDB 7
editor
author 4 10 9
section 8 5
chapter
XML Data
1-Index 1 6 2 3
book
title
paper
libraryDB 7
editor
author 10 9
section 8 5
chapter 4
In tree structured Data, strong Dataguide and 1-Index coincide

21. 2/T-Index 2-Index T-Index To support queries of x1Px2 ex) //title
Equivalence relation (≡)
(v, u) ≡ (v’, u’) iff L(v,u) =L(v’,u’)
where L(x,y) = {w| w is a label path from x to y}
Summary of path information bwt. two arbitrary nodes
T-Index
Generalization of 1/2-Index
(v1,…,vn )≡ (u1,…,un) iff L(v1,…,vn) =L(u1,…,un)
Conceptually similar to Access Support Relations
Support only predefined paths

22. Index Fabric [Cooper, Sample, Franklin, Hjaltason, Shadmon, VLDB 01]
Tree Structured Data
Conceptual similar to strong DataGuide
Layered structure
Use Patricia trie to index a large number of search keys
The simple path of an element which has a data value is encoded as a special character sequence
Keeps the key which is the combination of encoded sequence and data value.

23. Index Fabric P 1 1 2 … 2 8 Patricia Trie
“L”
“LBC” C B P
Patricia Trie 1 2 L B P T A …
LBAauthor1
LBTtitle1 C
XML Data
Keeps only the information of elements which have data values
Patricia trie : lossy Compression

24. ToXin [Rizzolo, Mendelzon: WebDB 01] Tree Structured Data
Conceptually Similar to strong DataGuide (not minimal DataGuide)
Support navigation of forward and backward traversal
Path Tree ( = strong DataGuide)
A node of Path Tree has an Index Table or Value Tables
Index Table (IT): parent-child relationships
Value Table (VT): owner-value relationships

25. ToXin Index Tables Value Tables …
XML Data
Index Tables
LibraryDB:IT
book:IT
paper:IT
title:VT
author:VT
chapter
section
LibararyDB
parent child
null
LibraryDB.book
parent child
LibraryDB.paper
parent child
Value Tables
LibraryDB.book.author
parent value
author1 …
Since ToXin keeps parent-child relationships, ToXin supports path expression with value predicates
ex) /libraryDB/book[author = author1]

26. A(k)-Index [Kaushik, Shenoy, Bohannon, Gudes: ICDE 02]
Strong DataGuide and 1-Index record the all simple paths
Increase index size => Increase search space
Approximation of 1-Index
Non-deterministic
Utilize local similarity(= degree k)
reduce the size of index graph

27. A(k)-Index k-bisimulation (≈k)
For any two nodes, v and u, v ≈0 u iff u and v have the same label
Node v≈ku iff v≈k-1u and for every parent v’ of v, there is a parent u’ of u such that v’≈k-1u’ A C B D E
XML Data
A(0)-Index
A(1)-Index
A(2)-Index (= 1-Index)

28. A(k)-Index Building cost = O(km) In general, for 1-Index, k < logm
Query Processing
label path expression whose length ≤ k+1
precise
label path expression whose length > k+1
safe : include false results
validation => require the data scan

29. APEX: Adaptive Path indEx for XML Data
[Chung, Min, Shim : SIGMOD 02]
Strong DataGuide and 1-Index are kept the all simple paths
Users used partial matching path queries
//book/title
Exhaustive navigation of index structure for partial matching path queries may result in performance degradation

30. APEX Deterministic Approximation of DataGuides
Efficient processing of partial matching path queries
Workload-Aware
Self Tuning Strategies [Chaudhuri et. al 00]
Utilize Query Workload
Build APEX with both XML data and frequently used paths
Sequential pattern mining [Agrawal and Srikant 95]

31. frequently used paths = {book.title}
APEX
libraryDB
title
paper
book
&1
&2
&3
&8
&9
&0
author
&4
&5
chapter
&6
section
&7
editor
APEX
frequently used paths = {book.title}
label
xnode
next
xroot
&0
libraryDB
&1
book
&2
paper
&3
title
author
&4
chapter
&5
section
&6
editor
&7
label
count
xnode
next
book
&8
remainder
&9
extent
&0: {<null,0>} &1: {<0,1>} &2: {<1,2> }&3: {<1,6>}
&4: {<2,4>, <6,8>, <6,9>} &5: {<2,5>}
&6: {<6,10>} &7: {<2,8>} &8: {<2,3>} &9: {<6,7>}
Hash Tree
keep frequently used paths
prevent the exhaustive search
Graph Structure
structural summary + extents
XML Data

32. F&B Index [Kaushik, Bohannon, Naughton, Korth : SIGMOD 02]
Support Twig path expression
/A/B[C]
Basic Idea
For every edge e labelled l from v to u, add an (inverse) edge e-1 with label l-1 from u to v
And then, compute 1-Index on this modified graph.
Very large Index space
Apply some heuristics
Exploiting Local Similarity : k-bisimulation A B C A B
C-1

33. Discussion Path Index Future Work
Improve the query performance by restriction of search space
Can be apply to various application
Selectivity Estimation
QBE(Query By Example)
Future Work
Support twig queries
Query Optimization
cost formula of path index

34. Reference
C. Chung, J. Min and K. Shim, “ APEX: An Adaptive Path Index for XML Data,” SIGMOD 02
B. Cooper, N. Sample, M. Franklin, G. Hjaltason and M. Shadmon, “A Fast Index for Semistructed Data,” VLDB 01
M. Garofalakis, A. Gionis, R. Rastogi, S. Seshadri, and K. Shim, “ XTRACT: A System for Extracting Document Type Descriptors from XML Documents,” SIGMOD 00
L. Goldman and J. Widom, “ DataGuides: Enabling Queries Formulation and Optimization in Seminstructured Databases,” VLDB 97
R. Kaushik, P. Bohannon, J. Naughton and H. Korth, “Covering Indexes for Branching Path Queries,” SIGMOD 02
R. Kaushik, P. Shenoy, P. Bohannon and E. Gudes, “Exploiting Local Similarity for Indexing Paths in Graph-Structured Data,” ICDE 02
A. Kemper and G. Moerkotte, “Access Support Relations: An Indexing Method for Object Bases,” Information Systems 92
T. Milo and D. Suciu, “ Index Structures for Path Expressions,” ICDT 99
S. Nestorov, J. Ullman, J. Wiener and S. Chawathe, “ Representative Objects : Concise Representations of Semi structured, Hierarchical Data,” ICDE 97
F. Rizzolo and A. Mendelzon,” Indexing XML Data with ToXin,” WebDB 01
R. Paige and R. Tarjan, “Three partition refinement algorithms,” SIAM Journal of Computing 87
P. Valduriez, “Join Indices,” TODS 87