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DEXA, Sept. 3, 2001R. Bayer, TUM1 XML Databases: Modelling and Multidimensional Indexing Rudolf Bayer Sept. 3, 2001.

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Presentation on theme: "DEXA, Sept. 3, 2001R. Bayer, TUM1 XML Databases: Modelling and Multidimensional Indexing Rudolf Bayer Sept. 3, 2001."— Presentation transcript:

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2 DEXA, Sept. 3, 2001R. Bayer, TUM1 XML Databases: Modelling and Multidimensional Indexing Rudolf Bayer Sept. 3, 2001

3 DEXA, Sept. 3, 2001R. Bayer, TUM2 XML Document as an XML Tree MISTRAL Rudolf Bayer Techn. Univ. Volker Markl FORWISS UB-tree POT Region a piece of text more text Fenk Ramsak DW Queries

4 DEXA, Sept. 3, 2001R. Bayer, TUM3 XML Basics 1.Every XML document is an ordered tree with labeled branches, many potential representations 2.The structure of the tree is described by a DTD 3.Parsing a document is trivial w.r. to wellformedness or conformance with a given DTD

5 DEXA, Sept. 3, 2001R. Bayer, TUM4 DTD for the Document <DOCTYPE Paper [ <!ELEMENT Paper (Title, Authors*, Keyword*, Abstract?, Text, BibRec*)> ]

6 DEXA, Sept. 3, 2001R. Bayer, TUM5 Operations with Trees store in rel. DBMS find documents based on path search predicates retrieve parts of found documents insert and delete documents in a DB modify documents, i.e. delete and insert subtrees of a document Note: in RDBMS we deal with complete tuples, in XML we deal with partial documents

7 DEXA, Sept. 3, 2001R. Bayer, TUM6 Path Notation and Identical Paths [1] Bayer [2] Markl Distinguish paths by repetition numbers, in document fixed by order of the text  Paths become unique within a document, use them as attributes in a universal relation XML-Rel

8 DEXA, Sept. 3, 2001R. Bayer, TUM7 Universal Relation XML-Rel: with Attribute Paths APi Did AP1 AP2 AP3...Apk Use path notation for attributes: Paper/Authors[2]/LNMarkl Every document is exactly one tuple in XML-Rel with unbounded number of attributes

9 DEXA, Sept. 3, 2001R. Bayer, TUM8 Document with DTD and Data Instance Paper TitleMISTRAL Authors* FNRudolfVolker LNBayerMarkl AffiliationTUFORWISS Keywords*UB-treePOT Region Abstracta piece of text Textmore text BibRec* Authors* LNFenkRamsak TitleDW Queries

10 DEXA, Sept. 3, 2001R. Bayer, TUM9 DTD with Numbering per Level and Repetition Numbers Paper 1 TitleMISTRAL 2 Authors*[1][2] 1 FNRudolfVolker 2 LNBayerMarkl 3 AffiliationTUFORWISS 3 Keywords*[1][2][3] UB-treePOT Region 4 Abstracta piece of text 5 Textmore text 6 BibRec*[1] 1 Authors*[1][2] 2 LNFenkRamsak 2 TitleDW Queries

11 DEXA, Sept. 3, 2001R. Bayer, TUM10 Surrogate-Patterns and Path-Expressions: 1 1 Surr-PPath-ExpressionsExamples of Paths 1Title 2.*Authors* Authors[1], Authors[2],… 2.*.1Authors*/FNAuthors[1]/FN 2.*.2Authors*/LNAuthors[1]/LN 2.*.3Authors*/Affiliation 3*Keywords* 4Abstract 5Text 6.*BibRec* 6.*.1.*BibRec*/Authors* BibRec[1]/Authors[1], … 6.*.2BibRec*/Title BibRec[1]/Title, … Surrogate patterns reflect ordering!

12 DEXA, Sept. 3, 2001R. Bayer, TUM11 SomePaths, Values Surrogates TitleMISTRAL1 Authors[1]/FNRudolf2[1]1 Authors[1]/LNBayer2[1]2 Authors[1]/AffiliationTechn. Univ.2[1]3 Authors[2]/FNVolker2[2]1... Keywords[3]Region3[3] Abstracta piece of text4... BibRec[1]/Authors[2]/LN Ramsak6[1]1[2]1 BibRec[1]/TitleDW Queries6[1]2 Note: from surrogates and values we can reconstruct the original document with the help of an additional surrogate to tag mapping, which is stored in an additional table

13 DEXA, Sept. 3, 2001R. Bayer, TUM12 Mapping for XML-Rel: XML-Rel with Attribute Paths APi Did AP1 AP2 AP3...APk is mapped to XML-Quad Did Attr-PathValueSurrogate with candidate keys (Did, Attr-Path) or (Did, Surrrogate)

14 DEXA, Sept. 3, 2001R. Bayer, TUM13 Decompose XML Quad into two relations Type-Dim to replace Attribute-Paths by Surrogates Attr-PathSurrogateType and relation XML-Ind for XML Index Did SurrogateValue define view XML-Quad as select Did, Surrogate, Attr-Path, Value from Type-Dim T, XML-Ind X where T.Surrogate = X.Surrogate

15 DEXA, Sept. 3, 2001R. Bayer, TUM14 Relation XML-Ind for decomposed XML-Quad DidSurrogateValue 71MISTRAL 72[1]1Rudolf … 2[2]1Volker 2[2]2Markl 2[2]3FORWISS 3[1]UB-Tree 3[2]POT 3[3]Region 4a piece of text 5more text 6[1]1[1]2Fenk 6[1]1[2]2Ramsak 76[1]2DW Queries

16 DEXA, Sept. 3, 2001R. Bayer, TUM15 Observations lexicographic ordering of surrogates properly represents document order subtrees, like for Author[2] correspend to intervals of surrogates very compact representation of XML documents 3-dimensional table most queries have 2 restrictions

17 DEXA, Sept. 3, 2001R. Bayer, TUM16 User Queries and DML Statements select Paper/Title from XML-Rel where Paper/Authors[1]/LN = ‘Bayer’ Note: if the repetition number of the author is not known, we write where Paper/Authors[$i]/LN = ‘Bayer’ in order to instantiate the variable [$i] properly

18 DEXA, Sept. 3, 2001R. Bayer, TUM17 Rewriting the XML-Rel Query select Paper/Title from XML-Rel where Paper/Authors[1]/LN = ‘Bayer’ is rewritten into 2 queries: select Did into Did-Set from XML-Quad where Attr-Path = ‘Paper/Authors[1]/LN’ and Value = ‘Bayer’; select Value from XML-Quad where Attr-Path = ‘Paper/Title’ and Did in Did-Set

19 DEXA, Sept. 3, 2001R. Bayer, TUM18 Another Rewriting of the XML-Rel Query select Paper/Title from XML-Rel where Paper/Authors[1]/LN = ‘Bayer’ is rewritten into a single join-query: select Q2.value from XML-Quad Q1, XML-Quad Q2 where (Q1.Attr-Path = ‘Paper/Authors[1]/LN’ and Q1.Value = ‘Bayer’) and (Q2.Did = Q1.Didand Q2.Attr-Path = ‘Paper/Title’)

20 DEXA, Sept. 3, 2001R. Bayer, TUM19 General Join Rewriting of XML-Rel to XML-Quad select APi, APj from XML-Rel where APk = c1 and APl = c2 Is rewritten into: select T3.Value, T4.Value from XML-Quad T1, XML-Quad T2, XML-Quad T3, XML-Quad T4 where T1.Attr-Path = ‘APk’ and T1.Value = c1 and T2.Attr-Path = ‘APl’ and T2.Value = c2 and T3.Attr-Path = ‘APi’ and T4.Attr-Path = ‘APj’ and and T1.Did = T2.Did and T2.Did = T3.Did and T3.Did = T4.Did

21 DEXA, Sept. 3, 2001R. Bayer, TUM20 Transformation of previous Query select T3.Value, T4.Value from XML-Quad T1, XML-Quad T2, XML-Quad T3, XML-Quad T4 where T1.Attr-Path = ‘APk’ and T1.Value = c1 and T2.Attr-Path = ‘APl’ and T2.Value = c2 and T1.Did = T2.Did T3.Attr-Path = ‘APi’ and T3.Did = T1.Did T4.Attr-Path = ‘APj’ and T4.Did = T1.Did

22 DEXA, Sept. 3, 2001R. Bayer, TUM21 UB-Trees: Multidimensional Indexing geographic databases (GIS) Data-Warehousing: Star Schema all relational databases with n:m relationships mobile, location based applications XML R S n m (r, s)

23 DEXA, Sept. 3, 2001R. Bayer, TUM22 Typical Queries on XML-Quad Did Attr-PathValueSurrogate find documents written by Markl Leads to two restrictions: Attr-Path = ‚Author[$i]/LN‘ and Value = ‚Markl‘ Retrieve Title of found documents with Did = k Again two restrictions: Attr-Path = ‚Title‘ and Did = k Change spelling errror from ‚Rudolph‘ to ‚Rudolf‘ in Did 1274 Did = 1274 and Attr-Path = Author[1]/FN  Suitable for mulitdimensional indexing!!

24 DEXA, Sept. 3, 2001R. Bayer, TUM23 Basic Idea of UB-Tree linearize multidimensional space by space filling curve, e.g. Z-curve or Hilbert use Z-address as key to store objects in B-Tree  Response time for query is proportional to size of the answer!

25 DEXA, Sept. 3, 2001R. Bayer, TUM24 UB-Tree: Regions and Query-Box Z-region [0.1 : 1.1.1]

26 DEXA, Sept. 3, 2001R. Bayer, TUM25 World as self balancing UB-Tree

27 DEXA, Sept. 3, 2001R. Bayer, TUM26 QB1: select Paper/Titlewhere Paper/Authors[1]/LN = ‘Markl’ Rewriting results in a 2-dimensinal restriction, i.e. a line query LQ where Attr-Path = ‚Paper/Authors[1]/LN‘ and Values = ‚Markl‘

28 DEXA, Sept. 3, 2001R. Bayer, TUM27 Title... LN „Markl“ Values Attr-Path or Surrogate Did line query LQ Title line

29 DEXA, Sept. 3, 2001R. Bayer, TUM28 Assumptions: for the analysis of queries 10 6 documents with 10 4 B each this results in a DB of 10 GB with 10 6 pages  Each dimension of a 3 dimensional cube spans about 100 pages, i.e. D = 100 i.e. the number of pages „skewered“ by LQ

30 DEXA, Sept. 3, 2001R. Bayer, TUM29 Algorithm and Complexity for QB1: for each hit h on line query LQ there is a document d(h) finding all hits isO(D) d(h) corresponds to a plane slice s(h) intersecting O(D 2 ) pages Title correspond to a line through s(h) therefore only O(D) pages must be fetched from s(h) Complexity per retrieved hit: O(D) ~ 1 sec/hit  Response time = size of answer * 1 sec/hit

31 DEXA, Sept. 3, 2001R. Bayer, TUM30 Query QB2: “Get Titles and Authors of papers, in which papers coauthored by Markl and Ramsak are cited” select D1/Paper/Title, D1/Paper/Authors* from Documents D1, Documents D2 where D1/Paper/BibRec[$i]/Authors[$j]/LN = ‘Markl’ and D2/Paper/BibRec[$k]/Authors[$m]/LN = ‘Ramsak’ and D1/Paper/BibRec[$i] = D2/Paper/BibRec[$k] Note: the last (join) condition is checked on the surrogates of D1...BibRec and D2...BibRec (note that several variables: Paper, $i and BibRec are instantiated by this) and the projection list is retrieved via a generalized Tetris algorithm

32 DEXA, Sept. 3, 2001R. Bayer, TUM31 Title Authors LN „Markl“ Values Attr-Path Did „Ramsak“

33 DEXA, Sept. 3, 2001R. Bayer, TUM32 Classification and Complexity of Queries n no restriction, i interval of breadth , c constant, D 3 = P = number of pages in DB Assumption: P = 10 6 pages = 8 GB, D = 100, 300 pages per second from disk, time estimates in seconds, restrictions 10% or less.

34 DEXA, Sept. 3, 2001R. Bayer, TUM33 RestrQuery-Box# of pagesTime n n nuniverseD 3 < 3000 i n nslice  D 3 or D 2 < 300or 30 for plane i i npillar  1  2 D 3 or D< 30or 1 for line i i ibox  1  2  3 D 3 < 3 c n nplane D 2 < 30 c i nstripe  1 D 2 < 3 c i irectangle  1  2 D 2 < 1 c c nline D< 1 c c iline interval  1 D< 1 c c cpoint const< 1

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