1. KAIST2002 SIGDB Tutorial1 Indexing Methods for Efficient XML Query Processing Jun-Ki Min KAIST http://islab.kaist.ac.kr/~jkmin/

2. KAIST2002 SIGDB Tutorial2 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

3. KAIST2002 SIGDB Tutorial3 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. KAIST2002 SIGDB Tutorial4 XML Example title1 author1 … title2 author2 author3 … … 1 6 2 3 book title paper libraryDB 7 editor title author 4 109 section 8 author 5 chapter author ToXinIndex FabricAPEX

5. KAIST2002 SIGDB Tutorial5 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 => inefficiency Structural Summary & Path Index by restricting the search to only relevant portions of XML Data

6. KAIST2002 SIGDB Tutorial6 Schemas for XML DTD, XML Schema Specifies the constraints of XML Data are not mandatory => lack of external schema Structural Summary Summary of label paths Path Index Structural Summary + Extents

7. KAIST2002 SIGDB Tutorial7 Schemas for XML Applications User Interface XML Data Design, Editing Query Formulation Query Validation Query Optimization Path Index

8. KAIST2002 SIGDB Tutorial8 Structural Summary DTD Extraction XTRACT based on element information Structural Summary Representative Objects based on path information

9. KAIST2002 SIGDB Tutorial9 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. KAIST2002 SIGDB Tutorial10 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. KAIST2002 SIGDB Tutorial11 Representative Objects(RO) book title paper libraryDB editor title author section author chapter author XML Data name book title paper libraryDB editor title authorsection authorchapter Graph Representation of 1-RO name book title paper libraryDB editor title author section author chapter Graph Representation of 2-RO(= Full-RO) name

12. KAIST2002 SIGDB Tutorial12 Path Index Access Support Relations Deterministic Strong DataGuide Index Fabric ToXin APEX Non-Deterministic 1-Index A(k) Index F&B Index

13. KAIST2002 SIGDB Tutorial13 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. KAIST2002 SIGDB Tutorial14 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. KAIST2002 SIGDB Tutorial15 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 C A B CC AB C Various DataGuides A B C CCCC B An XML Data

16. KAIST2002 SIGDB Tutorial16 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 A C B CC A C B C 2 3 4 5 6 1 2,4 3,5 6 5 1 A A C B CC 2 3 4 5 6 C Source Strong DataGuide A B C 1 2,4 3,5 6 C

17. KAIST2002 SIGDB Tutorial17 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 = /l 1 /l 2 / … /l n Non-deterministic Based on backward bisimulation which is originated from graph verification Extents are disjoint More compact size than Strong DataGuides

18. KAIST2002 SIGDB Tutorial18 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 ) 1. If x≈ b y and x is the root then y is the root 2. Conversely, If x≈ b y and y is the root, then x is the root. 3. If x≈ b y and is an edge, then there is exists an edge (y ’ l y), such that x ’ ≈ b y ’ 4. Conversely, if x≈ b y and (y ’ l y) is an edge, then there exists an edge (x ’ l x) such that x ’ ≈ b y ’

19. KAIST2002 SIGDB Tutorial19 ≡ vs ≈ b X ≡ Y since L X = L Y = {a.b.d, a.c.d} X Y v ≈ b u  v ≡ u O(mlogm) construction cost [Paige and Tarjan 87] d d aa aa bbc c d XY ≈b≈b

20. KAIST2002 SIGDB Tutorial20 1-Index vs Strong DataGuide In tree structured Data, strong Dataguide and 1- Index coincide 1 6 2 3 book title paper libraryDB 7 editor title author 4109 section 8 author 5 chapter author XML Data 1 6 2 3 book title paper libraryDB 7 editor title author 10 8,9 section 8 5 chapterauthor Strong DataGuide 4 1-Index 1 6 2 3 book title paper libraryDB 7 editor title author 10 9 section 8 5 chapterauthor 4

21. KAIST2002 SIGDB Tutorial21 2/T-Index 2-Index To support queries of x 1 Px 2 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 (v 1, …,v n )≡ (u 1, …,u n ) iff L(v 1, …,v n ) =L(u 1, …,u n ) Conceptually similar to Access Support Relations Support only predefined paths

22. KAIST2002 SIGDB Tutorial22 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. KAIST2002 SIGDB Tutorial23 Index Fabric Keeps only the information of elements which have data values Patricia trie : lossy Compression XML Data Patricia Trie 0 1 22 L B P TA … LBAauthor1LBTtitle1 C … 2 1 2 8 “L” “LBC” C B P C

24. KAIST2002 SIGDB Tutorial24 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. KAIST2002 SIGDB Tutorial25 ToXin Since ToXin keeps parent-child relationships, ToXin supports path expression with value predicates ex) /libraryDB/book[author = author1] LibraryDB:IT book:ITpaper:IT title:VT author:VT chapter title:VT author:VT section LibararyDB parent child null 1 LibraryDB.book parent child 1 2 LibraryDB.paper parent child 1 6 LibraryDB.book.author parent value 2 author1 … Index Tables Value Tables XML Data

26. KAIST2002 SIGDB Tutorial26 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. KAIST2002 SIGDB Tutorial27 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≈ k u iff v≈ k-1 u and for every parent v ’ of v, there is a parent u ’ of u such that v ’ ≈ k-1 u ’ A CB D E D E A C B D E XML DataA(0)-Index A CB D E D A(1)-Index A CB D E D E A(2)-Index (= 1-Index) D E

28. KAIST2002 SIGDB Tutorial28 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. KAIST2002 SIGDB Tutorial29 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. KAIST2002 SIGDB Tutorial30 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. KAIST2002 SIGDB Tutorial31 APEX Hash Tree keep frequently used paths prevent the exhaustive search Graph Structure structural summary + extents APEX frequently used paths = {book.title} extent &0: { } &1: { } &2: { }&3: { } &4: {,, } &5: { } &6: { } &7: { } &8: { } &9: { } labelxnodenext xroot&0 libraryDB&1 book&2 paper&3 title author&4 chapter&5 section&6 editor&7 labelcountxnodenext book&8 remainder&9 libraryDB title paper book &1 &2 &3 &8 &9 &0 author &4 &5 chapter &6 section &7 editor XML Data

32. KAIST2002 SIGDB Tutorial32 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 ABC ABC -1

33. KAIST2002 SIGDB Tutorial33 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

34. KAIST2002 SIGDB Tutorial34 Thank You! Any Question? http://islab.kaist.ac.kr/~jkmin jkmin@islab.kaist.ac.kr

35. KAIST2002 SIGDB Tutorial35 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