Databases and Information Systems 1

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1 Databases and Information Systems 7. XML storage and core XPath implementation 7.. Mapping XML to relational databases and Datalog how to store an XML document in a relation database? how to answer XPath queries on these XML documents? minimum information needed to store and to query XML documents? 7.. A succint data format for XML implementing core XPath use this for XML compression ( also in Section 9 ) Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation /

2 Implementing XML by relational databases many different approaches one approach is based on label, firstchild (fc) and nextsibling(ns) <> <></> <>pc00</> </> pc00 Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation /

3 Implementing XML by relational databases many different approaches one based on label, firstchild (fc) and nextsibling(ns) <> <></> <>pc00</> </> label(, Label) fc(p,fc) Label() pc00 fc() Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation / ns(,ns) ns() pc00

4 Implementing XML axes by Datalog programs followingsibling(x,y) = ns + (X,Y) ; // implementation in datalog as usual followingsibling(x,y) : ns( X, Y ). followingsibling(x,y) : ns( X, NS ), followingsibling(ns,y). child(x,y) : fc(x,y). child(x,y) : fc(x,fc), followingsibling( FC, Y ). Label() fc() pc00 pc00 Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation / ns(,ns) ns()

5 Implementing XML axes by Datalog programs // followingsibling(x,y) = ns + (X,Y). // implementation in datalog as usual followingsibling(x,y) : ns( X, Y ). followingsibling(x,y) : ns( X, NS ), followingsibling(ns,y). child(x,y) : fc(x,y). child(x,y) : fc(x,fc), followingsibling( FC, Y ). // descendant( X, Y ) = child + (X,Y). descendant(x,y) : child( X, Y ). descendant(x,y) : child( X, C ), descendant(c,y). pc00 Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation /

6 Implementing XML axes by Datalog programs reverseaxis(x,y) = reverseaxis (Y,X) ancestor( D, A ) : descendant( A, D ). parent( C, P ) : child ( P, C ). parent( A, P ) : attribute ( P, A ). parent( N, P ) : namespace ( P, N ). Axisorself(X,Y) = Axis(X,Y) Axisorself(X,Y) = self(x,y) pc00 self( X, X ). descendantorself( A, D ) : descendant( A, D ). descendantorself( A, D ) : self( A, D ). ancestororself( D, A ) : ancestor( D, A ). ancestororself( D, A ) : self( D, A ). Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation /

7 Implementing XML axes by Datalog programs following::* = ancestororself::* / followingsibling::* / descendantorself::* following(x,y) : ancestororself(x,a), followingsibling(a,s), descendantorself(s,y). preceding(x,y) : following(y,x). pc00 Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation / 7

8 Implementing XPath queries by Datalog queries //? goal(k). goal(k) : label( R, ), descendant( R, K ), label( K, ). Answer: K =. ( R = ) pc00 Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation / 8

9 Implementing XPath queries by Datalog queries //? goal(k). goal(k) : label( R, ), descendant( R, K ), label( K, ). Answer: K =. ( R = ) // [ ] /? goal( K ). goal(k) : label( R, ), ( R = ) descendant( R, A ), ( A = ) child( A, P ), label( P, "" ), ( P = ) child( A, K ), label( K, "kunde" ). ( K = ) pc00 Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation / 9

10 Evaluation of XPath implemented by Datalog. translate core XPath expression into a datalog program: using all the core XPath axes. datalog program contains tables fc(firstchild), ns(nextsibling), label plus datalog rules for reducing other axes to these eleemntary axes, e.g. followingsibling( X,Y ) : ns( X, Y ). followingsibling( X,Y ) : ns( X, NS ), followingsibling( NS, Y ).. evaluate Datalog program using fast algorithm for Datalog evaluation, that combines TopDown selectionfirst evaluation with setoriented bottomup computation, e.g. Process Model only unary and binary base relations subclass of Datalog programs that can be evaluated efficiently Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation / 0

11 Summary: XML/XPath implemented by Datalog base relations for binary XML tree: Label(, Label ), fc( Parent, FirstChild ), ns( Node, NextSibling ) recursive deductive database rule systems for followingsibling( Node, FS ) child( Parent, Child ), descendant( Node, Descendant ) combination rules for following( Node, Following ) descendantorself( Node, DOS ) ancestororself( Node, AOS ) reverseaxis Datalog rules for ancestor( Node, Ancestor ) parent( Node, Parent ) precedingsibling( Node, PrecedingSibling ) preceding( Node, Preceding ) Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation /

12 Generating and storing a binary XML tree How to transfrom an XML document such that we can answer core XPath queries with only fc, ns and label? transform XML document into Binary Simple SAX Events: XML file SAX Events Simple SAX Events (convert to elements only) Binary Simple SAX Events (Details given on the following slides) Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation /

13 How to treat different node types? escape text nodes: <E>"text"</E> <E> <=text> </=text> </E> escape attribute nodes: <E a="value"></e> <E> <=value> </=value> </E> + escape node, comments, PIs only elements remain Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation /

14 From SAX to a Simple SAXParserAPI () 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 // generate Simple SAX events, i.e. elements, for attribute name, // i.e. atts.getqname(i), and attribute value, i.e. atts.getvalue(i) } } // 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 { } Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation /

15 From SAX to a Simple SAXParserAPI () // SAX parser calls this once // for each text constant 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(); // generate Simple SAX event, i.e. element, for the text constant } Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation /

16 How to transform XML into a binary XML tree. Simplify single node type (element nodes) only. generate binary tree and store binary tree fc E fc E E E ns ns fc E ns E E7 ns E8 OR: generate and process binary SAX events ( next slide) Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation /

17 From SAX events to binary SAX events Pairs of SAXEvents Location Step Generate event endelement( _ ) startelement( a ) nextsibling :: a nextsibling :: a startelement( _ ) startelement( a ) firstchild :: a firstchild :: a endelement( _ ) endelement( _ ) startelement( _ ) endelement( _ ) parent :: * no location step (nothing) go back to parent (nothing) Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation / 7

18 Conclusions: XML/XPath implemented by Datalog only the following base relations or Simple SAX Events are needed: Label(, Label ), fc( Parent, FirstChild ), ns( Node, NextSibling ) remaining XPath evaluation can be done by evaluation of datalog rules when storage format is changed, only implement Label, fc, ns If compressed XML supports implementation of Label, fc, ns, then core XPath can be evaluated ( topic of chapters 7. and 9 ) Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation / 8

19 Storage models for XML trees (): binary tables for binary trees based on label, firstchild (fc) and nextsibling(ns) as in Section 7. <> <></> <>pc00</> </> label(, Label) fc(p,fc) Label() fc() pc00 pc00 Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation / 9 ns(,ns) ns()

20 Storage models for XML trees (): a single table for binary trees based on label, firstchild (fc) and nextsibling(ns) <> <></> <>pc00</> </> Label() fc() ns() pc00 pc00 Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation / 0

21 Storage models for XML trees (): a single table for unranked trees based on label, firstchild (fc) and nextsibling(ns) <> <></> <>pc00</> </> Label() p() sibling pc00 pc00 Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation /

22 Ex.: Compute needed storage for XML trees () three tables binary tree () single table binary tree () single table unranked tree Label() fc() Label() fc() ns() Label() p() sibling ns() pc00 pc00 pc00 Assume: byte per, fc(), ns() and bytes on average per Label. compute sizes for (), () and (). develop general formulas for binary XML tree with N inner nodes: a) how many leaf nodes? b) formulas for () and for (). How can we store an unranked tree in (more) tables? Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation /

23 Intermediate summary: Storage of XML trees different storage models binary tree can be efficiently stored different implementations: multiple tables, single table we use single table because of further compression steps Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation /

24 Using arrays to store XML trees () three tables binary tree () single table binary tree () single table unranked tree Label() fc() Label() fc() ns() Label() p() sibling ns() pc00 pc00 pc00 Use as array index st column is not needed how to reduce high values? use relative s / array indices (array index difference) instead of absoulte s Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation /

25 Succinct storage of XML trees () single table binary tree Label() fc() ns() ns pc00 pc00 How can we avoid pointers? use array instead of table avoids first column use bits denoting existence of fc and ns avoids fc and ns columns, but requires bits Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation /

26 Succinct storage of XML trees () use bits denoting existence of fc and ns avoid pointers single table binary tree Label() fc() ns() ns pc00 pc00 <r> <A> <K> <=M> </=M> </K> <P> <=p> </=p> </P> </A> </r> tags bits node s Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation /

27 Succinct storage of XML trees () use bits denoting existence of fc and ns avoid pointers <r> <A> <K> <=M> </=M> </K> <P> <=p> </=p> </P> </A> </r> tags bits node s Label() pc00 Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation / 7

28 Succinct storage of XML trees () Exercise. How can we support navigation via firstchild (fc) and nextsibling (ns)?. How can we compress further without disabling navigation? <r> <A> <K> <=M> </=M> </K> <P> <=p> </=p> </P> </A> </r> tags bits node s Label() pc00 Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation / 8

29 Succinct storage of XML trees (). How can we support navigation via firstchild (fc) and nextsibling (ns)?. How can we compress further without disabling navigation? <r> <A> <K> <=M> </=M> </K> <P> <=p> </=p> </P> </A> </r> tags bits node s Label() pc00. store actual position fc : look at next bit = fc exists ns : close following subtree, i.e. s = 0s and look at next bit = ns exists. count s until actual position node Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation / 9

30 Summary and Conclusions XPath evaluation can be implemented in Datalog, if XML storage format supports fc, ns, label XML storage in a relational database: store relationships fc, ns, label in table(s) succinct storage of XML: store tag sequence in bitstream (nesting) + 'label list' (labels) bit stream supports fc, ns 'label list' and bit stream position support label Preprocessing of the XML input: XML document SAXEvents Binary Simple SAX Events Databases and Information Systems WS 008 / 09 Prof. Dr. Stefan Böttcher XML storage and XPath implementation / 0