Databases and Information Systems 2

(1)

Databases and Information Systems 2 - SS 20 07 - Prof. Dr. Stefan Böttcher - Storage models for XML trees / 1

Databases and Information Systems 2

Storage models for XML trees

in small main memory devices

Long term goals:

reduce memory

Æ

compression (?)

still query efficiently

Æ

small data structures

Storage models for XML trees (1):

binary tables for binary trees

Auftrag 2 root 1 Meier 4 pc500 6 PC 5 Kunde 3 Label(ID) ID 3 2 2 1 6 5 4 3 fc(ID) ID

• based on label, first-child (fc) and next-sibling(ns) <Auftrag>

<Kunde>Meier</Kunde> <PC>pc500</PC> </Auftrag>

label( ID, Label) fc(P,FC)

Kunde Auftrag PC Meier pc500 root

1

2

3

4

5

6

5 3 ns(ID) ID ns(ID,NS)

(2)

Storage models for XML trees (2):

a single table for binary trees

Auftrag 2 root 1 Meier 4 pc500 6 PC 5 Kunde 3 Label(ID) ID

• based on label, first-child (fc) and next-sibling(ns) <Auftrag> <Kunde>Meier</Kunde> <PC>pc500</PC> </Auftrag> Kunde Auftrag PC Meier pc500 root

1

2

3

4

5

6

-3 -2 -6 5 4 ns(ID) fc(ID)

Storage models for XML trees (3):

a single table for unranked trees

Auftrag 2 root 1 Meier 4 pc500 6 PC 5 Kunde 3 Label(ID) ID

• based on label, first-child (fc) and next-sibling(ns) <Auftrag> <Kunde>Meier</Kunde> <PC>pc500</PC> </Auftrag> Kunde Auftrag PC Meier pc500 root

1

2

3

4

5

6

1 1 -1 3 1 5 2 2 1 2 sibling p(ID)

(3)

Ex.: Compute needed storage for XML trees

Auftrag 2 root 1 Meier 4 pc500 6 PC 5 Kunde 3 Label(ID) ID 1 1 -1 3 1 5 2 2 1 2 sibling p(ID)

(3) single table

unranked tree

Auftrag 2 root 1 Meier 4 pc500 6 PC 5 Kunde 3 Label(ID) ID -3 -2 -6 5 4 ns(ID) fc(ID)

(2) single table

binary tree

Auftrag 2 root 1 Meier 4 pc500 6 PC 5 Kunde 3 Label(ID) ID 3 2 2 1 6 5 4 3 fc(ID) ID 5 3 ns(ID) ID

(1) three tables

binary tree

Assume: 1 byte per ID, fc(ID), ns(ID) and 5 bytes on average per Label 1. compute sizes for (1), (2) and (3)

2. develop general formulas for binary XML tree with N inner nodes:

a) Æhow many leaf nodes?

b) Æformulas for (1) and for (2)

3. How can we store an unranked tree in (more) tables ?

Using arrays to store XML trees

Auftrag 2 root 1 Meier 4 pc500 6 PC 5 Kunde 3 Label(ID) ID 1 1 -1 3 1 5 2 2 1 2 sibling p(ID)

(3) single table

unranked tree

(2) single table

binary tree

Auftrag 2 root 1 Meier 4 pc500 6 PC 5 Kunde 3 Label(ID) ID 3 2 2 1 6 5 4 3 fc(ID) ID 5 3 ns(ID) ID

(1) three tables

binary tree

Use ID as array indexÆ1st column is not needed

how to reduce high ID values?

use relative IDs / array indices (array index difference) instead of absoulte IDs

(4)

How to treat different node types?

escape attribute nodes:

<E a="value"></E>

Æ

<E>

<@a>

<=value>

</=value>

</@a>

</E>

escape text nodes:

<E>"text"</E>

Æ

<E>

<=text>

</=text1>

</E>

+ escape root node, comments, PIs

Æ

only elements remain

How to transform XML into a binary XML tree

1. Simplify

Æ

single node type (element nodes) only

2. generate binary tree

3. store binary tree

E1

E3

E4

E2

(5)

How to transform XML into a binary XML tree

1. Simplify

Æ

single node type (element nodes) only

2. generate binary tree

3. store binary tree

E1

E3

E4

E2

E5

E6

E7

E8

fc

ns

_fc

ns

XML file

Æ

SAX-Events

Æ

Simplified SAX events

Æ

Binary Simplified SAX events

Æ

list storing binary simplified SAX events

Æ

…

(6)

Simple Access to XML (SAX)

Parser accesses at most one XML element node at a time:

- can navigate and process nodes only in document order

Æless flexible programming than DOM

+ need less space in main memory

+ loading document nodes into main memory is fast

doc

customer

address

order order address

name = “Alice“

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

1. <doc> 2. <customer name=“Alice“> 3. <order> 4. 5. 6. ... </order> 7. <address> </address> </customer> 8. <customer> 9. <order/> 10. <address/> </customer> </doc>

SAX-Parser-Java-API (1)

// generate JAXP SAXParserFactory

SAXParserFactory spf = SAXParserFactory.newInstance();

// set namespaceAware to true

spf.setNamespaceAware(true);

// generate JAXP SAXParser

SAXParser saxParser = spf.newSAXParser();

// get handle to the embedded SAX XMLReader

XMLReader xmlReader = saxParser.getXMLReader();

// generate new SAX output stream for ContentHandler of XMLReader

xmlReader.setContentHandler(new SAXOut());

// setup ErrorHandler, before parsing starts

xmlReader.setErrorHandler(new MyErrorHandler(System.err));

// parse the XML file using the XMLReader

(7)

SAX-Parser-Java-API (2)

// Parser calls this procedure once, when parsing the document starts

public void startDocument() throws SAXException { …} // SAX parser calls this once for each start tag of an element

public void startElement( String namespaceURI, String localName, String qName, Attributes atts)

throws SAXException { … // code example: for(int i=0; i<atts.getLength(); i++) { // for each attribute

out.println( atts.getQName(i) + "=\"" + atts.getValue(i)+"\""); } // output attribute name and attribute value

… }

// SAX parser calls this once for each end tag of an element

public void endElement( String namespaceURI, String localName, String qName) throws SAXException { …} // SAX parser calls this once when end of document is reached

public void endDocument() throws SAXException { … }

SAX-Parser-Java-API (3)

// SAX parser calls this once

// for each text found in the XML document

public void characters(char[ ] ch, int start, int length) throws SAXException

{

String text = new String (ch, start, length); text = text.trim();

… }

(8)

Pairs of SAX-Events

Location Step

Generate node

end-element(_)

start-element(a)

start-element(_)

start-element(a)

end-element(_)

start-element(_)

end-element(_)

next-sibling :: a

next-sibling : a

first-child :: a

first-child : a

parent :: *

(nothing)

go back to parent

no location step

(nothing)

From SAX events to binary SAX events

different storage models

binary tree can be efficiently stored

different implementations:

multiple tables,

single table

we use single table because of further compression steps

Summary: Storage of XML trees

(9)

How can we avoid pointers ?

use array instead of table

Æ

avoids first column

use bits denoting existence of fc and ns

Æ

avoids fc and ns columns, but requires bits

Succinct storage of XML trees (1)

single table

binary tree

1

2

3

4

5

6 ns

use bits denoting existence of fc and ns

Æ

avoid pointers

Succinct storage of XML trees (2)

single table

binary tree

1

2

3

4

5

6 ns

<r> <A> <K> <=M> </=M> </K> <P> <=p> </=p> </P> </A> </r> tags 1 1 1 1 0 0 1 1 0 0 0 0 bits

(10)

use bits denoting existence of fc and ns

Æ

avoid pointers

Succinct storage of XML trees (3)

ID Label(ID) 1 Æroot 2 ÆAuftrag 3 ÆKunde 4 ÆMeier 5 ÆPC 6 Æpc500

1 2 3 4 5 6 node IDs

1. How can we support navigation via first-child (fc) and next-sibling (ns)? 2. How can we compress further without disabling navigation?

Succinct storage of XML trees (4) - Exercise

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Succinct storage of XML trees (5)

1 2 3 4 5 6 node IDs

1. store actual position

fc : look at next bit

Æ

1 = fc exists

ns : close following subtree, i.e. |1s| = |0s|

and look at next bit

Æ

1 = ns exists

2. count 1s until actual position

Æ

node ID

1. How can we support navigation via first-child (fc) and next-sibling (ns)? 2. How can we compress further without disabling navigation?

Succinct storage of XML trees (6)

1 2 3 4 5 6 node IDs

Succinct representation of IDs in table ( ID , Label(ID) ) TID concept lenght Label(ID) 4 Æroot 7 ÆAuftrag 5 ÆKunde 5 ÆMeier 2 ÆPC 5 Æpc500

zip packages

packages' size e.g. 20

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Succinct storage of XML trees (7)

1 2 3 4 5 6 node IDs

Succinct representation of IDs in table ( ID , Label(ID) ) TID concept lenght Label(ID) 4 Æroot 7 ÆAuftrag 5 ÆKunde 5 ÆMeier 2 ÆPC 5 Æpc500 zip packages

packages' size e.g. 20 Æ?

Æstore / search only 1, 4, 7 (IDs that start a new package)

Tuple IDentifier (TID) concept for strings

lenght Label(ID) 4 Æroot 7 ÆAuftrag 5 ÆKunde 5 ÆMeier 2 ÆPC 5 Æpc500