1. Management of XML and Semistructured Data
Lecture 2, Wednesday, 4/4/2001

2. Outline Semistructured data XML Simulation Bisimulation Syntax
Data model

3. The Semistructured Data Model
Bib
&o1
complex object
paper
paper
book
references
&o12
&o24
&o29
references
references
author
page
author
year
author
title
http
title
author
publisher
title
author
author
&o43
&25
&96
1997
last
firstname
atomic object
firstname
lastname
first
lastname
&243
&206
“Serge”
“Abiteboul”
“Victor”
122
133
“Vianu”
Object Exchange Model (OEM)

4. Syntax for Semistructured Data
May omit oid’s:
{ paper: { author: “Abiteboul”,
author: { firstname: “Victor”,
lastname: “Vianu”},
title: “Regular path queries …”,
page: { first: 122, last: 133 } }

5. Set Semantics for Trees
Want to say that {a, a, b} = {a, b}
Define equality for trees first, then for graphs
Definition Two trees t, t’ are equal, t=t’, if:
They are both atomic values with same value
t = {t1, ..., tm}, t’ = {t1’, ..., tn’} and:
i=1,...,m, j=1,...,n s.t. ti = tj’
j=1,...,n, i=1,...,m s.t. ti = tj’

6. Set Semantics: Exampleb b = a a b c c d c d c c c c c d 1 2 2 1 1 1 1 2 e e e 3 3 3

7. Set Semantics for Graphs
Previous definition does not apply directly to graphs with cycles
Need to adapt it  bisimulation
First, we will define a simulation

8. Note: if we insist that R be a function  graph homeomorphism
Graph Simulation
Definition Two edge-labeled graphs G1, G2
A simulation is a relation R between nodes:
if (x1, x2)  R, and (x1,a,y1)  G1,
then exists (x2,a,y2)  G2 (same label)
s.t. (y1,y2)  R x1 x2 a R G1 G2 y1 a R y2
Note: if we insist that R be a function  graph homeomorphism

9. Graph Bisimulation Definition Two edge-labeled graphs G1, G2
A bisimulation is a relation R between nodes s.t. both R and R-1 are simulations

10. Set Semantics for Semistructured Data
Definition Two rooted graphs G1, G2 are equal if there exists a bisimulation R from G1 to G2 such that (root(G1), root(G2))  R
Notation: G1  G2
For trees, this is precisely our earlier definition

11. Examples of Bisimilar Graphs= c c c a a = a a a a
...

12. Examples of non-Bisimilar Graphsc b c
This is a simulation but not a bisimulation
Why ?
Notice: G1, G2 have the same sets of paths

13. Examples of Simulation
Simulation acts like “subset”
{a, b}  {a, b, c}
{a, b:{c}}  {d, a:{e,f}, b:{c,g}}
Question:
if DB1  DB2 and DB2  DB1 then DB1  DB2 ? c a a b b d a a b b e c g f c

14. Facts About a (Bi)Simulation
The empty set is always a (bi)simulation
If R, R’ are (bi)simulations, so is R U R’
Hence, there always exists a maximal (bi)simulation:
Checking if DB1=DB2: compute the maximal bisimulation R, then test (root(DB1),root(DB2)) in R

15. Computing a (Bi)Simulation
Computing the maximal (bi)simulation:
Start with R = nodes(G1) x nodes(G2)
While exists (x1, x2)  R that violates the definition, remove (x1, x2) from R
This runs in polynomial time ! Better:
O((m+n)log(m+n)) for bisimulation
O(m n) for simulation
Compare to finding a graph homeomorphism !

16. XML a W3C standard to complement HTML origins: structured text SGML
motivation:
HTML describes presentation
XML describes content
(version 2, 10/2000)

17. From HTML to XML
HTML describes the presentation

18. HTML <h1> Bibliography </h1>
<p> <i> Foundations of Databases </i>
Abiteboul, Hull, Vianu
<br> Addison Wesley, 1995
<p> <i> Data on the Web </i>
Abiteoul, Buneman, Suciu
<br> Morgan Kaufmann, 1999

19. XML XML describes the content <bibliography>
<book> <title> Foundations… </title>
<author> Abiteboul </author>
<author> Hull </author>
<author> Vianu </author>
<publisher> Addison Wesley </publisher>
<year> 1995 </year>
</book> …
</bibliography>
XML describes the content

20. XML Terminology tags: book, title, author, …
start tag: <book>, end tag: </book>
elements: <book>…<book>,<author>…</author>
elements are nested
empty element: <red></red> abbrv. <red/>
an XML document: single root element
well formed XML document: if it has matching tags

21. More XML: Attributes <book price = “55” currency = “USD”>
<title> Foundations of Databases </title>
<author> Abiteboul </author> …
<year> 1995 </year>
</book>
attributes are alternative ways to represent data

22. More XML: Oids and References
<person id=“o555”> <name> Jane </name> </person>
<person id=“o456”> <name> Mary </name>
<children idref=“o123 o555”/>
</person>
<person id=“o123” mother=“o456”><name>John</name>
oids and references in XML are just syntax

23. More XML: CDATA Section
Syntax: <![CDATA[ .....any text here...]]>
Example:
<example> <![CDATA[ some text here </notAtag> <>]]>
</example>

24. More XML: Entity References
Syntax: &entityname;
Example: <element> this is less than < </element>
Some entities:
<
>
&
&
&apos; ‘
" “
&
Unicode char

25. More XML: Processing Instructions
Syntax: <?target argument?>
Example: <product> <name> Alarm Clock </name> <?ringBell 20?> <price> </price> </product>
What do they mean ?

26. More XML: Comments Syntax <!-- .... Comment text... -->
Yes, they are part of the data model !!!

27. XML Namespaces http://www.w3.org/TR/REC-xml-names (1/99)
name ::= [prefix:]localpart
<book xmlns:isbn=“
<title> … </title>
<number> 15 </number>
<isbn:number> …. </isbn:number>
</book>

28. XML Namespaces syntactic: <number> , <isbn:number>
semantic: provide URL for schema
<tag xmlns:mystyle = “ …
<mystyle:title> … </mystyle:title>
<mystyle:number> …
</tag>
defined here

29. XML Data Model Several competing models: Document Object Model (DOM):
(2/2001)
class hierarchy (node, element, attribute,…)
objects have behavior
defines API to inspect/modify the document
XSL data model
Infoset
PSV (post schema validation)
XML Query data model (next)

30. XML Query Data Model http://www.w3.org/TR/query-datamodel/ 2/2001
Describes XML as a tree, specialized nodes
Uses a functional-style notation (think ML)

31. XML Query Data Model
Node ::= DocNode | ElemNode | ValueNode | AttrNode | NSNode | PINode | CommentNode | InfoItemNode | RefNode

32. XML Query Data Model Element node (simplified definition):
elemNode : (QNameValue, {AttrNode }, [ ElemNode | ValueNode])  ElemNode
QNameValue = means “a tag name”
{...} = means “set of...”
[...] = means “list of ...”

33. XML Query Data Model
Reads: “give me a tag, a set of attributes, a list of elements/values, and I will return an element”

34. XML Query Data Model Example
book1= elemNode(book, {price2, currency3}, [title4, author5, author6, author7, year8])
price2 = attrNode(…) /* next */ currency3 = attrNode(…) title4 = elemNode(title, string9) …
<book price = “55”
currency = “USD”>
<title> Foundations … </title>
<author> Abiteboul </author>
<author> Hull </author>
<author> Vianu </author>
<year> 1995 </year>
</book>

35. XML Query Data Model Attribute node:
attrNode : (QNameValue, ValueNode)  AttrNode

36. XML Query Data Model Example
price2 = attrNode(price,string10) string10 = valueNode(…) /* next */ currency3 = attrNode(currency, string11) string11 = valueNode(…)
<book price = “55”
currency = “USD”>
<title> Foundations … </title>
<author> Abiteboul </author>
<author> Hull </author>
<author> Vianu </author>
<year> 1995 </year>
</book>

37. XML Query Data Model Value node:
ValueNode = StringValue | BoolValue | FloatValue …
stringValue : string  StringValue
boolValue : boolean  BoolValue
floatValue : float  FloatValue

38. XML Query Data Model Example
price2 = attrNode(price,string10) string10 = valueNode(stringValue(“55”)) currency3 = attrNode(currency, string11) string11 = valueNode(stringValue(“USD”))
title4 = elemNode(title, string9) string9 = valueNode(stringValue(“Foundations…”))
<book price = “55”
currency = “USD”>
<title> Foundations … </title>
<author> Abiteboul </author>
<author> Hull </author>
<author> Vianu </author>
<year> 1995 </year>
</book>

39. XML v.s. Semistructured Data
both described best by a graph
both are schema-less, self-describing

40. Similarities and Differences
<person id=“o123”>
<name> Alan </name>
<age> 42 </age>
< > </ >
</person>
{ person: &o123
{ name: “Alan”,
age: 42, } }
<person father=“o123”> …
</person>
{ person: { father: &o123 …} }
person
name
age
Alan 42
father
similar on trees, different on graphs

41. More Differences XML is ordered, ssd is not
XML can mix text and elements:
<talk> Making Java easier to type and easier to type
<speaker> Phil Wadler </speaker>
</talk>
XML has lots of other stuff: entities, processing instructions, comments
Very important: these differences make XML data management harder

42. Summary of Data Models semistructured data, XML
data is self-describing, irregular
schema embedded with the data