M02107

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AN X M L ALGEBRA FOR

ON LI N E PROCESSI N G OF

X M L D OCUM EN TS

By : H a n dok o a n d Ja n u sz R. Ge t t a

Ou t lin e

v

Int roduct ion

v

Relat ed Work

§ XML Data Model & Algebra exists

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XM L St ruct ures

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XM L Algebra

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Conclusion & Fut ure w orks

I n t r odu ct ion - M ot iv a t ion

v Since XM L document accept ed as a st andard in Informat ion Syst em, online processing of semist ruct ured dat a becomes more import ant . v Online processing applies online algorit hm w hich

process dat a piece by piece.

v The performance of semist ruct ured dat a processing is affect ed by some aspect s:

§ Semistructured data has more complex structure than columns and rows.

§ Data model exists requires data to be completed before can be processed, while online processing needs to process data piece-by-piece.

§ In some of data model exists, semistructured data is treated as relational-type data model:

• Evaluations of XML Stream are in tuple-based approach. • Unnestand nestoperations have to be employed. • Requires more resources of CPU and memory

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An Ex a m ple of On lin e Pr oce ssin g - On lin e I n t e gr a t ion

APPLI CATI ONS D AT A

SOUR CES D AT A SOUR CES

PREVI OUS RESULT RECENT DATA

INCLUDES:

1. Fragmentation Handling 2. XML Algebra

3. Execution Plan Algorithms 4. Scheduling Algorithms

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Re la t e d W or k -

X M L D a t a M ode l & Alge br a

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XM L Algebra (XAL) [4]

§ XML as rooted connected directed graph cyclic or acyclic

§ Vertices represent elements, edges represent simple values

§ Has three groups of operators:

• Extractionoperators

– Projection, Selection, distinct, join, sort, product

• MetaOperators

– Map, Kleene Star

• Construction operator

– Create vertex, create edge, copy

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Lit e r a t u r e Re v ie w -

v

XAnsw er [6]

§ Algebra in relational-like data structure

§ Uses data structure called Envelope <he|be|re>

§ Header heis unordered set of attribute (A), body beis a set of pair (A,v) where vis value, and rerepresents result

§ XAnswer provides Unary operators (Function Execution,

selection, projection, sort, index, nest, unnest, and duplicate) and Binary operators such as union, cross product, and left outer joinoperators.

§ Union operator in XAnswer does not remove duplicates.

§ XAnswer also provides left-outer-join operation instead of expressing it using selection, cross product and union operators.

Lit e r a t u r e Re v ie w -

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TAX (Tree Algebra for XM L)[5]

§ Represents the document in an ordered labeled tree. Every XML element will be represented as a node which has:

• tagattribute: single-valued attribute which indicates the type of element;

• contentattribute: representing atomic value which can be any of atomic types;

• pedigreeattributes: carry the information of element's predecessor which will be very useful for manipulation and comparison.

§ TAX proposed an idea of tree pattern (TP) but represents a very different concept from classical relational algebra.

§ TAX provides Selection, Projection, Product, Grouping,

Aggregation, Renaming, Reordering, Copy and Paste, Value Updates, Node Deletion and Node Insertion operation,and some set operators.

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X M L D a t a M ode l –

Ex t e n de d Tr e e Gr a m m a r

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A st ruct ure of an XM L document is a pair <ETG, EIG> w here ETG(Ext ended Tree Grammar)

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Ex a m ple of ETG a n d it s se n t e n ce

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X M L D a t a M ode l –

Ex t e n de d I n st a n ce Gr a m m a r

Applying EI G t o ETG sent ence

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When w e get any t erminal symbol library(...) t hen w e apply it t o product ion rule w hich mat ch t o t he t erminal symbol. library(x)_→<library>x</library>

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x in st ep 1 consist s of nodes books and aut hors at t he same level, so w e need t o apply t he

corresponding product ion rules

books(x)_→<books>x</books> and authors(x)_→<authors>x</authors>

Our inst ance XM L document w ill become:

</library>

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As reaching a t erminal symbol w hich has no inner st ruct ure (t erminal w hich is not follow ed by

opening curly bracket ), w e t ranslat e it int o relat ed product ion rule. For example

title_→<title>#PCDATA</title> w ill be t ranslat ed

int o: <title>Basic XML</title>

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Terminal symbol w it h no inner st ruct ure and follow ed by square bracket ([) w ill be t ranslat ed using product ion rules defined. For example

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X M L D a t a M ode l – I n de x e d ETG

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Then w e ext end ETG t o accommodat e recursive st ruct ures as:

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X M L Alge br a

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XM L algebra in t his syst em consist s of: § Basic operations

• Restructuring Operation (π) • Filtering Operation (σ) • Cross Product operation (×) § Set Operations (∪,∩, and -)

§ Derived Operations (join, semijoin, and antijoin)

X M L Alge br a - Su b Gr a m m a r

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Let G_iand G_jbe ETGs. Let G_jincludes t he follow ing produc on rules Y

→

t_y{r_y(X)}, X

→

t_x{r_x(Z)}, Z

→

t_z{r_z} w here r_y(X) is a regular expression t hat includes a non-t erminal symbol X and r_x(Z) is a regular

expression t hat includes a non-t erminal symbol Z.

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We say t hat G_iis a sub-grammar of G_jw hen G_ican be obt ained from G_jby t he applicat ion of t he follow ing t ransformat ion rules:

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X M L Alge br a – Su b gr a m m a r

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Transformat ion of document st ruct ure:

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X M L Alge br a - Re st r u ct u r in g

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Rest ruct uring operat ion can be defined as:

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Alg or it h m f or Re st r u ct u r in g

X M L Alge br a - Filt e r in g

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Filt ering operat ion can be defined as:

Definit ion 8. Filt ering is an unary operat or denot ed as

σ

_ϕ(D) = {R₁,R₂, …,R_D: Ri

∈

X, w here D is a set of docum ent s,

ϕ

is a t riple <P,min,max>, P is a valid pat h, min is t he minimum occurrence of P (default -1), and max is t he maximum occurrence of P

(default -1).

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To different iat e bet w een preserve and remove semant ics of t he operat or, w e int roduce t he symbols

σ

+_and

σ

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X M L Alge br a – Cr oss Pr odu ct

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Cross product is a binary operat or w hich creat es all possible pairs of t he document s from t w o set s.

Definit ion 9. Cross product is defined as

Rx_ρS = {

ρ

{r s}:r

∈

R

∧

s

∈

S, w here R and S are set s of document ;

ρ

is a valid name of element w hich w ill be t he parent node of every combinat ion of

document s from R and S.

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Algor it h m for Cr oss Pr odu ct

Tr e e Pa t t e r n r e pr e se n t a t ion

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N={BOOK,YEAR,AUTHOR}

T={book,year,aut hor}

A={}

S={BOOK}

P={BOOK→book{YEAR AUTHOR+},

YEAR→year,

AUTHOR→aut hor}

Qu e r y a ddit ion

v

Rat her difficult t o do query:

§ retrieve all books which have at most 1 author

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X M L Alge br a – On lin e Pr oce ssin g

v The argument s of t he XM L algebra are set s of document s, and w e assume t hat every increment / decrement of an argument is an XM L document

v For online int egrat ion, consider an int egrat ion as a UNION operat ion, w e should be able t o comput e

increment / decrement dat a (δ_Ai) and int egrat e t he result w it h t he previous one:

e(A₁,…,A_i⊕δ_Ai,…,A_D) = e(A₁,…,A_i,…,A_D) ⊕f(A₁,…,δ_Ai,…,A_D) v Example, applying U over ⊕:

e(R₁⊕δ₁)UR₂= (R₁UR₂) ⊕ δ₁

v fis a funct ion t hat need t o be defined so t hat all operat ors over increment / decrement dat a follow s t he form.

v We found t hat f is a funct ion of eit her ⊕or -.

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Con clu sion

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XM L Algebra proposed is consist ent w it h relat ional algebra.

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It meet s t he need of online processing:

§ It works in tree structure to avoid nestand unnestoperations.

§ It possible to find a function to process increment data

Re fe r e n ce s

[1] C. Beeri and Y. Tzaban. SAL: An algebra for semist ruct ured dat a and XM L. In Informal Proc. Of Workshop on The Web and Dat abases, ACM SIGM OD, pages 37{42. ACM Press, 1999.

[2] S. Bose, L. Fegaras, D. Levine, and V. Chaluvadi. A query algebra for fragment ed XM L st ream dat a. In Proceeding of 9t h Int ernat ional Conference on Dat a Base Programming Languages (DBPL), pages 275{277, Pot sdam, Germany, Sept ember 6-8 2003.

[3] G. Burat t i. A M odel and an Algebra for Semi-St ruct ured and Full-Text Queries. PhD t hesis, Informat ica, Universit a di Bologna, Padova, 2007.

[4] F. Frasincar, G.-J. Houben, and C. Pau. XAL: an algebra for XM L query opt imizat ion. Aust . Comput . Sci. Commun., 24(2):49{56, January 2002.

[5] H. V. Jagadish, L. V. S. Lakshmanan, D. Srivast ava, and K. Thompson. TAX: A t ree algebra for XM L. In In Proc. DBPL Conf, pages 149{164, 2001.

[6] M . Lukichev, B. Novikov, and P. M ehra. An XM L-algebra for eficient set -at -a-t ime execu-a-t ion. ComSIS, 9(1):64{80, January 2012.

[7] M . M urat a, D. Lee, M . M ani, and K. Kaw aguchi. Taxonomy of XM L schema languages using formal language t heory. ACM Trans. Int ernet Technol., 5(4):660{704, Nov. 2005.

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Re se a r ch Pr ogr e ss

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A st ruct ure of an XM L document can be formally defined by a Regular Tree Grammar

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Re se a r ch Pr ogr e ss

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We int roduce a grammar for creat ing inst ance XM L document w hich is called Inst ance Grammar (IG). IG is a cont ext sensit ive grammar w hich is

t ransformat ion of regular t ree grammar sent ences int o inst ances of XM L document .

X M L D a t a M ode l –

Re gu la r Tr e e Gr a m m a r

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A st ruct ure of an XM L document can be formally defined by an RTG (Regular Tree Grammar).

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X M L D a t a M ode l – I n st a n ce Gr a m m a r

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