Indexing Methods for Efficient XML Query Processing

1
Indexing Methods for Efficient XML Query
Processing

• Jun-Ki Min
• KAIST
• http//islab.kaist.ac.kr/jkmin/

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XML

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

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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

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XML Example
ltlibraryDBgt ltbook editor 1gt lttitlegt title1
lt/titlegt ltauthorgt author1 lt/authorgt
ltchaptergt lt/chaptergt lt/bookgt ltpapergt
lttitlegt title2lt/titlegt ltauthor id 1gt
author2 lt/authorgt ltauthorgt author3 lt/authorgt
ltsectiongt lt/sectiongt lt/papergt lt/libraryDBgt
ToXin
Index Fabric
APEX
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XML Query

• XML Query Language
• 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 gt inefficiency
• Structural Summary Path Index
• by restricting the search to only relevant
  portions of XML Data

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Schemas for XML

• DTD, XML Schema
• Specifies the constraints of XML Data
• lt!ELEMENT book (title, author,chapter)gt
• are not mandatory
• gt lack of external schema
• Structural Summary
• Summary of label paths
• Path Index
• Structural Summary Extents

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Schemas for XML

• Applications
• User Interface
• XML Data Design, Editing
• Query Formulation
• Query Validation
• Query Optimization
• Path Index

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Structural Summary

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

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XTRACT

• Garofalakis, Gionis, Rastogi, Seshadri, Shim
  SIGMOD 00
• Infer concise and accurate DTD
• Choose a DTD from candidate DTDs
• (a b),(b a) gt (ab) 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)33 12
• 9(for DTD)11 11

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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
  k1 exist in data.
• 1-RO
• Simplest very compacted representation

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Representative Objects(RO)
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Path Index

• Access Support Relations
• Deterministic
• Strong DataGuide
• Index Fabric
• ToXin
• APEX
• Non-Deterministic
• 1-Index
• A(k) Index
• FB Index

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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 IndexValduriez 87
• Based on the paths in the schema
• Materialize access paths of arbitrary length
• Support only predefined subsets of paths.

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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

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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

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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

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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

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1-Index

• Equivalence relation ()
• 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 xby and x is the root then y is the root
• Conversely, If xby and y is the root, then x is
  the root.
• If xby and ltxl xgt is an edge, then there is
  exists an edge (yl y), such that x by
• Conversely, if xby and (yl y) is an edge, then
  there exists an edge (xl x) such that xby

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vs b
a
a
a
a
c
b
b
c
d
d
d
X
Y

• 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

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1-Index vs Strong DataGuide

• In tree structured Data, strong Dataguide and
  1-Index coincide

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2/T-Index

• 2-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

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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.

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Index Fabric
XML Data

• Keeps only the information of elements which have
  data values
• Patricia trie lossy Compression

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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

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ToXin
XML Data

• Index Tables

LibararyDB parent child null 1
LibraryDB.book parent child 1 2
LibraryDB.paper parent child 1 6

• Value Tables

• LibraryDB.book.author
• parent value
• author1

• Since ToXin keeps parent-child relationships,
  ToXin supports path expression with value
  predicates
• ex) /libraryDB/bookauthor author1

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A(k)-Index

• Kaushik, Shenoy, Bohannon, Gudes ICDE 02
• Strong DataGuide and 1-Index record the all
  simple paths
• Increase index size gt Increase search space
• Approximation of 1-Index
• Non-deterministic
• Utilize local similarity( degree k)
• reduce the size of index graph

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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 vku iff vk-1u and for every parent v of
  v, there is a parent u of u such that vk-1u

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A(k)-Index

• Building cost O(km)
• In general, for 1-Index, k lt logm
• Query Processing
• label path expression whose length k1
• precise
• label path expression whose length gt k1
• safe include false results
• validation gt require the data scan

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APEXAdaptive 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

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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

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APEX
APEX frequently used paths book.title
extent 0 ltnull,0gt 1 lt0,1gt 2 lt1,2gt
3 lt1,6gt 4 lt2,4gt, lt6,8gt, lt6,9gt 5
lt2,5gt 6 lt6,10gt 7 lt2,8gt 8
lt2,3gt 9 lt6,7gt

• Hash Tree
• keep frequently used paths
• prevent the exhaustive search
• Graph Structure
• structural summary extents

XML Data
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FB Index

• Kaushik, Bohannon, Naughton, Korth SIGMOD 02
• Support Twig path expression
• /A/BC
• 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-1
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Discussion

• Path Index
• 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

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Thank You!

• Any Question?
• http//islab.kaist.ac.kr/jkmin
• jkmin_at_islab.kaist.ac.kr

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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