1. Management of XML and Semistructured Data
Lecture 9: Schemas
Friday, April 27, 2001

2. Outline Schemas for semistructured data Schemas for XML unordered

3. Schemas for Relational v.s. SS Data
Schemas in relational data:
Defined before the data
Strictly enforced
Schemas in SS data
Defined after the data
May not be enforced (some data doesn’t have schema)

4. When the Schema is Created
Created by the user
Before or after the data
Does not need to be unique
Extracted from the data
Unheard of in relational databases
Extracted from the query
Like type inference in programming languages
Different schema formalisms for each task !

5. Schemas for Unordered Data
OEM
Cycles
Schema itself will be a graph

6. Schemas: An Example Some database: &r1 &c1 &c2 &s2 &s3 &s6 &s7 &s10
company
name
address
url
“Widget”
“Trenton”
“Gadget” “
“Paris”
&p2
&p1
&p3
&s0
&s1
&s4
&s5
&s8
&s9
person
“Smith”
name
position
phone
“Manager”
“Jones”
“ ”
“Dupont”
“Sales”
employee
manages
c.e.o.
works-for
&a1
&a2
&a3
&a4
&a5
&a6
&a7
description
procurement
salesrep
contact
task
eval
1997
1998
“on target”
“below target”

7. Graph Schemas Root person company works-for managed-by Employee
c.e.o. | employee
name | address | url
name | phone | position
string
description
Any *
Upper Bound Schema

8. The Two Questions to Ask
Conformance: does that data conform to this schema ?
Classification: if so, then which objects belong to what classes ?

9. Graph Simulation Definition Two edge-labeled graphs G1, G2
A simulation is a relation R between nodes:
if (x1, x2) in R, and (x1,a,y1) in G1,
then exists (x2,a,y2) in G2 (same label)
s.t. (y1,y2) in R x1 x2 a R G1 G2 y1 a R y2

10. Using Simulation Data graph D, schema S
conformance: find maximal simulation R from D to S
Notation: D  S
classification: check if (x,c) in R
Notation: x  c

11. Example Database Graph Schema &r1 person person company manages person
Root
manages
person
person
company
works-for
&p1
employee
company
c.e.o.
&c1
&p2
&c2
c.e.o.
&p3
works-for
works-for
works-for
phone
position
managed-by
name
position
address
name
name
address
name
name
Company
Employee
&s0
&s1
&s2
&s3
&s4
&s5
&s6
url
&s7
&s8
&s9
description
c.e.o. | employee
“Smith”
“Manager”
“Widget”
“Trenton”
“Jones”
“ ”
“Gadget”
“Paris”
“Dupont”
“Sales”
name | address | url
description
&s10
name | phone | position
string
description
&a5
&a1 “
eval
1998
&a4
procurement
salesrep
1997
Any
task
&a7 *
&a2
&a3
&a6
contact
“below target”
“on target”
Database
Graph Schema

12. Formally Graph schema S is a graph, s.t.: Nodes are called classes
Edges are labeled with unary predicates, p(x) Examples:
person = “x=person”
name | address = “x=name  x=address”
* = “true”
int = “x int”
name = “x  name”

13. Examples of Graph Schemas (What Do They Mean ?)
person
person
S1=
description
name
name
age
age
string
int
string
int
 name   age
string  int
part
S3=
S1 = there are persons; each can have several names and several ages, of types string and int respectively
S2 = same as S1, plus persons can have description edges, under which we can have any edge with any label, except name and age
S3 = describes a hierarchy of parts and subparts, arbitrary deep. Leaf subparts (or parts) may have names and prices.
S4 = describes ANY database
S5 = persons may have name and age of types string, int, and under description there may be any structure.
S4=
subpart
name
price
person
description *
S5=
name
string
int
age
string
int
“Universal schema”, ST *

14. D = S = D  S person person person person person name age name name
string
int
Smith 55
D  S

15. Any database conforms to ST ! “Universal schema”*
Any database conforms to ST ! “Universal schema”

16. Schemas in SS Data v.s. Relational Data
Each data instance has exactly one schema
Semistructured data
One data instance has several schemas

17. The Classification Problem
D =
person
person
person
person
name
phone
name
name
phone
name
John
1234
Mary
string
string
string
string
Schema is nondeterministic: creates ambiguous classifications.

18. The Classification Problem
Definition A schema S is deterministic if for every class c and every label a, there is at most one outgoing edge labeled a from c
Fact: if S is deterministic and D is a tree, then each node is uniquely classified
(When D is not a tree, then this is not true.)

19. Deterministic Upper Bound Schemas
Given a schema S, we can always construct an deterministic approximation, Sd S=
person
person
Sd=
person
name
name
phone
phone
name
string
string
string
string
string
string
string
In general, Sd obtained by powerset constrcut  expensive

20. Lower Bound Schemas
Introduced (under a different name and formalism) in:
Nestorov, Abiteboul, Motwani, Extracting Schema from Semistructured Data, SIGMOD 98
Goal: extract some “schema” from the data
We will see later why these are “lower bound schemas”

21. Lower Bound Schemas Schema = datalog program with special form
Classes = predicates
Company(x) :- link(x,”c.e.o.”,y), Employee(y), link(x,”name”,z), String(z), link(x,”address”,u), String(u) Employee(x) :- link(x,”works-for”,y), Company(y), link(x,”managed-by”,z), Employee(z), link(x,”name”,u), String(u), link(x,”address”,v), String(v), Root(x) :- link(x,”company”,y), Company(y), link(x,”person”,z), Employee(z)
Maximal fixpoint, rather than minimal fixpoint ! (next)

22. Datalog Minimal Fixpoint
Standard datalog semantcis. Transform program to:
Company(x)  y. z. u.(link(x,”c.e.o.”,y), Employee(y), link(x,”name”,z), String(z), link(x,”address”,u), String(u) Employee(x)  y.z.u.v.(link(x,”works-for”,y), Company(y), link(x,”managed-by”,z), Employee(z), link(x,”name”,u), String(u), link(x,”address”,v), String(v)) Root(x)  y.z.(link(x,”company”,y), Company(y), link(x,”person”,z), Employee(z))
Compute minimal model. What is it ?

23. Datalog Minimal Fixpoint
Standard datalog semantcis. Transform program to:
Company(x)  y. z. u.(link(x,”c.e.o.”,y), Employee(y), link(x,”name”,z), String(z), link(x,”address”,u), String(u) Employee(x)  y.z.u.v.(link(x,”works-for”,y), Company(y), link(x,”managed-by”,z), Employee(z), link(x,”name”,u), String(u), link(x,”address”,v), String(v)) Root(x)  y.z.(link(x,”company”,y), Company(y), link(x,”person”,z), Employee(z))
Answer: the empty set !
Compute maximal model.

24. Lower-Bound Schemas Equivalent representation of schema: Root person
company
works-for
managed-by
Employee
Company
c.e.o.
address
name
name
string

25. Simulation Strikes Back
person
person
company
manages
person
company
works-for
Root
person
&p1
employee
c.e.o.
&c1
&p2
&c2
c.e.o.
&p3
company
works-for
works-for
name
works-for
position
name
phone
address
name
address
position
name
name
managed-by
&s0
&s1
&s2
&s3
&s4
&s5
&s6
url
&s7
&s8
&s9
description
Company
Employee
c.e.o.
“Smith”
“Manager”
“Widget”
“Trenton”
“Jones”
“ ”
“Gadget”
“Paris”
“Dupont”
“Sales”
description
&s10
address
name
name
&a5
string “
eval
1998
&a1
&a4
procurement
salesrep
1997
&a7
&a3
task
&a2
&a6
contact
“below target”
“on target”
Lower Bound
Database
A model of program P is precisely a simulation (and vice versa)

26. Summary: Lower v.s. Upper Bound Schemas
Tells us what edges are allowed
Lower bound schemas
Tell us what edges are required

27. Schema Extraction (From Data)
Problem statement
given data instance D
find the “most specific” schema S for D
In practice: S too large, need to relax
[Nestorov, Abiteboul, Motwani 1998]

28. Schema Extraction: Sample Data
Example database D =
&r
employee
employee
employee
employee
employee
employee
employee
employee
manages
manages
manages
manages
manages
&p1
&p2
&p3
&p4
&p5
&p6
&p7
&p8
managedby
managedby
managedby
managedby
managedby
worksfor
worksfor
worksfor
company
worksfor
worksfor
worksfor
worksfor
worksfor
&c

29. Lower Bound Schema Extraction
[NAM’98] approach:
Start with the schema given by the data (S = D):
Each node = a predicate = a class
Compute maximal fixpoint (PTIME)
Declare two classes equal iff they are equal sets
E.g. p4={&p1,&p4,&p6}, p6={&p1,&p4,&p6}, hence p1=p4
Equivalently, p=p’ iff p(&p’) and p’(&p)
. . .
p4(x) :- link(x, manages, y), p5(y), link(x, worksfor, z), c(z)
p5(x) :- link(x, managed-by, y), p4(y), link(x, worksfor, z), c(z)

30. Lower Bound Schema Extraction
Result S =
Root
&r
employee
company
employee
Bosses
&p1,&p4,&p6
manages
Regulars
&p2,&p3,&p5,&p7,&p8
worksfor
managedby
Company
&c
worksfor

31. Lower Bound Schema Extraction
Equivalently:
Compute the maximal simulation D  D
Can do in time O(m2)
Two nodes p, p’ are equivalent iff x  x’ and x’  x
Schema consists of equivalence classes
Remark: could use the bisimulation relation instead (perhaps is even better)

32. Upper Bound Schema Extraction
The extracted lower bound schema S is also an upper bound schema !
But: nondeterministic
Convert S  Sd
Alternatively, convert directly D  Dd = Sd
These are data guides [McHugh and Widom]

33. Upper Bound Schema Extraction
Result Sd =
Root
&r
employee
Employees
&p1,&p1,&p3,P4
&p5,&p6,&p7,&p8
company
managedby
manages
worksfor
Bosses
&p1,&p4,&p6
manages
Regulars
&p2,&p3,&p5,&p7,&p8
worksfor
managedby
Company
&c
worksfor

34. XML Document Type Definitions
part of the original XML specification
an XML document may have a DTD
terminology for XML:
well-formed: if tags are correctly closed
valid: if it has a DTD and conforms to it
validation is useful in data exchange

35. DTDs as Grammars <!DOCTYPE paper [
<!ELEMENT paper (section*)>
<!ELEMENT section ((title,section*) | text)>
<!ELEMENT title (#PCDATA)>
<!ELEMENT text (#PCDATA)>
]>
<paper> <section> <text> </text> </section>
<section> <title> </title> <section> … </section>
<section> … </section>
</section>
</paper>

36. DTDs as Schemas Not so well suited:
impose unwanted constraints on order <!ELEMENT person (name,phone)>
references cannot be constrained
can be too vague:
<!ELEMENT person ((name|phone| )*)>