XML Constraints:
Specification, Analysis, and Applications
Wenfei Fan
School of Informatics, University of Edinburgh
&
Network Data and Services Research, Bell Laboratories
1
Outline
 XML Specifications: types and integrity constraints
 Specification of XML constraints:
– keys, foreign keys, FDs
– absolute vs. relative constraints
 Analysis of XML constraints
– Consistency analysis
– Implication analysis
 Applications of XML constraints, and research issues
– Relational storage of XML data via constraint propagation
– Schema-directed XML integration
– Normal forms, query optimization, updates, data cleaning . . .
2
Introduction to XML specificaiton
 XML Specification:
– types
– integrity constraints
– the need for XML constraints
3
XML data - an example
Rooted, node-labeled tree
– elements: db, province, capital, city, subtree/sub-document
elements/subelements, e.g., the capital child of province
– @attributes: @name, @inProvince, carrying text
– text nodes, e.g., “Hasselt”
db
province
@name
city
province
...
capital
“Limburg”
capital
capital
“Hasselt”
@inProvince
“Limburg”
“others” @inProvince “Hasselt”
“Limburg”
4
XML specification: DTD (type)
 Production: constrains the subelement list of each element
<!ELEMENT
db
(province+, capital+)>
<!ELEMENT
province (city*, capital)>
 Attributes: uniquely identified by name for each element, unordered
province: @name,
capital:
@inProvince
db
province
@name
city
province
...
capital
“Limburg”
capital
capital
“Hasselt”
@inProvince
“Limburg”
“others” @inProvince “Hasselt”
“Limburg”
5
XML specification: integrity constraints
Keys and foreign keys (vs. relational constraints):
 key: the value of a @name uniquely identifies a province
province.@name

province
capital.@inProvince 
capital
 FK: @inProvince of a capital references @name of a province
capital.@inProvince 
province.@name
db
province
@name
city
province
...
capital
“Limburg”
“others” @inProvince “Hasselt”
“Limburg”
capital
capital
“Hasselt”
@inProvince
“Limburg”
6
XML specification
 A type (DTD) D
 A set of integrity constraints, 
Example:
 DTD D: structure of the document, vs. types in a PL
<!ELEMENT db
(province+, capital+)>
<!ELEMENT province (city*, capital)>
province.@name, capital.@inProvince
 Constraints  : defined in terms of data values across elements
province.@name
 province
capital.@inProvince  capital
capital.@inProvince  province.@name
7
Why XML constraints?
Supported by W3C XML standard, XML Schema
In databases (supported by SQL standard), constraints are:
 an essential part of the semantics of data,
 fundamental to conceptual design,
 useful for choosing efficient storage and access methods,
 central to update anomaly prevention, …
In the XML setting: constraints have proved useful in
 database storage of XML data (via constraint propagation),
 schema-directed database publishing/integration in XML,
 XML query optimization and formulation,
 design theory for XML specifications: normal forms
 data cleaning, …
8
Data exchange on the Web: XML publishing
Web
DTD
XML
constraints
XML
Q: XML view
DB1
DB2
All members of a community (or industry) agree on a schema and
exchange data w.r.t. the schema: e-commerce, health-care, ...
Schema-Directed XML Publishing/Integration:
 mapping data from traditional database to XML
 satisfying the predefined DTD and constraints
9
Data exchange on the Web: XML shredding
Web
XML
XML keys
XML
XML shredding
DB1
propagation
DB2
relational FDs
XML shredding:
 mapping XML data to relations
 relational design: normalization via constraint propagation from
XML to relations
– optimal relational storage of XML data
– semantic connection: query/update optimization
10
XML constraints
 Specification of XML constraints:
– keys, foreign keys, FDs
– absolute vs. relative constraints
11
absolute constraints
Absolute keys and foreign keys are to hold on the entire document.
province.@name
 province
capital.@inProvince  capital
capital.@inProvince  province.@name
Extensions of relational counterparts
db
province
@name
city
province
...
capital
“Limburg”
capital
capital
“Hasselt”
@inProvince
“Limburg”
“others” @inProvince “Hasselt”
“Limburg”
12
Absolute keys and foreign keys [PODS’00, 01]
 key: [X]  .
An XML document satisfies the key iff
 x y  ext() (l X (x.l = y.l)  x = y)
 foreign key (FK): a combination of an inclusion constraint
1[X]  2[Y], and a key 2[Y]  2 .
A document satisfies the FK iff it satisfies the key and
 x  ext(1 )  y  ext(2 ) (x[X] = y[Y])
– , 1 ,2: element types; X, Y: sets (lists) of attributes;
– ext(): the set of  elements in an XML document.
Equality issue:
 (string) value equality: when comparing attributes
 node identify: when comparing XML elements
Unary keys and foreign keys: defined in terms of single-attribute.
13
Relative constraints [WWW’01, PODS’02]
An XML tree specifies countries, provinces, province capitals.
 What is a key for a province?
 What does @inProvince of a capital reference?
db
...
country
province
...
capital
country
province
@name
“Belgium”
@name
“Limburg”
capital “Hasselt”@inProvince
@inProvince “Hasselt”
“Limburg”
“Limburg”
@name capital
“Limburg”
...
capital
@name
“Holland”
“Maastricht” @inProvince
“Limburg”
@inProvince “Hasselt”
“Limburg”
14
Examples of relative constraints
Relative constraints: on a subdocument rooted at a country:
key:
country (province.@name
 province)
country (capital.@inProvince  capital)
FK:
country (capital.@inProvince  province.@name)
Absolute: on the entire document: country.@name  country
db
...
country
province
...
capital
@name
country
province
“Belgium”
...
capital
@name
“Holland”
@name
capital “Hasselt” @inProvince @name capital “Maastricht”
@inProvince
“Limburg”
“Limburg”
“Limburg”
“Limburg”
@inProvince “Hasselt”
“Limburg”
@inProvince
“Limburg”
“Hasselt”
15
Relative keys and foreign keys
 key: (1[X]  1). An document satisfies the key iff
 c  ext()  y, z  ext(1)
( (y  c)  (z  c)  l X (y.l = z.l)  y = z)
 foreign key (FK): ( 1[X]  2[Y] ) and a key ( 2[Y]  2) .
A document satisfies the FK iff it satisfies the key and
 c  ext()  y  ext(1) (( y  c) 
 z  ext(2 ) ((z  c)  y[X] = z[Y] ))
where
 (y  c): y is a descendant of c (y in the subtree rooted at c);
 : context type;
 ext(): the set of  elements in an XML document.
16
Relative vs. Absolute
 Absolute constraints are a special case of relative ones:
country.@name  country  db ( country.@name  country )
absolute: a fixed context type -- the root type r
 Absolute constraints are scoped within the entire document;
whereas relative ones within the context of a subdocument.
country (province.@name
 province)
country (capital.@inProvince  capital)
country (capital.@inProvince  province.@name)
country.@name  country
Together they specify constraints on the entire document
 Beyond relational constraints; important for hierarchically
structured data: XML, scientific databases, biomedical data, ...
17
Define keys with path expressions
 XML data is hierarchically structured!
“name” as a key for employees of companies only: target set is
identified with a path expression: //company//employee
 XML data is semistructured: it may not have a DTD/schema!
– key paths may be missing or have multiple occurrences
key specification should be independent of types
db
company
dept
name
company
employee
employee
name
name
government
...
university
employee employee employee
name
@id
@id
@id
name
18
firstName
lastName
Absolute path constraints [WWW’01]
Absolute key: (Q,
{P1, . . ., Pk} )
 Path expressions Q, Pi: XPath, regular path expressions, …
 target path Q: to identify a target set [[Q]] of nodes on which the
key is defined (vs. relation)
 a set of key paths {P1, . . ., Pk}: to provide an identification for
nodes in [[Q]] (vs. key attributes)
 semantics: for any two nodes in [[Q]], if they have all the key
paths and agree on them by value equality (existential), then
they must be the same node (value equality and node identity)
Examples:
(//company//employees, {name, phone}) -- composite key
( //company//employees, {//@id})
-- multiple keys
(//., {@id})
-- capturing ID attributes in DTDs 19
Relative path constraints [WWW’01]
Relative key: (Q, K)
 path Q identifies a set [[Q]] of nodes, called the context path;
 K = (Q’,
{P1, . . ., Pk} ) is a key on sub-documents rooted at
nodes in [[Q]] (relative to Q).
Example.
(//country, (province, {@capital}))
(//country,
{@name}) -- absolute key
 Absolute keys are a special case of relative keys:
(Q, K) when Q is the empty path
 Similarly for foreign keys
Specification of XML constraints is more involved than its relational
counterparts
20
Keys and foreign keys in XML Schema
key: (Q,
{P1, . . ., Pk} )
 Path expressions Q, Pi: fragments of XPath
 Uniqueness and existence: for each node x in [[Q]] and each i
in [1, n], there exists a unique node yi reached via Pi, and yi is
either a text node or an attribute
Foreign keys: (Q,
 (S,
{P1, . . ., Pk} )  (S,
{S1, . . ., Sk} )
{S1, . . ., Sk} ) is a key
 Uniqueness and existence: both Pi and Si
The uniqueness and existence condition complicates the
consistency and implication analyses
Absolute constraint
21
Other constraints for XML
Functional dependencies: {P1, . . ., Pk}  {S1, . . ., Sk}
 Generalizations of relational FDs – for deriving an extension of
relational-schema normal forms
 Absolute constraints [Arenas and Libkin, PODS’02]
XIGs:  x1 …  xn ( B(x1, …, Xn) 
∨ (i  [1, l]) ( y1 …  yk
Ci (x1, …, xn, y1, …, yk))
 Generalization of relational embedded constraints
 B, Ci: conjunction of simple XPath expressions
 Subsuming relative keys and foreign keys (Deutsch and Tannen,
[KRDB’01])
22
Constraint analysis
 Analysis of XML constraints
– Consistency analysis
– Implication analysis
– Absolute, relative, path-expression constraints
23
Consistency of XML specifications
Given D: a DTD
: a set of integrity constraints over D
Consistency: Is there an XML document that both conforms to
D and satisfies ?
One wants to know whether XML specifications make sense!
Run-time check: attempts to validate documents with (D, ).
This would not tell us whether repeated failures are due to a bad
specification or problems with the documents
 static analysis is desirable
24
An inconsistent specification
The specification with D and  is inconsistent!
 DTD D:
<!ELEMENT db
(province+, capital+)>
<!ELEMENT province (city*, capital)>
province.@name, capital.@inProvince
 Constraints  :
province.@name
 province
capital.@inProvince  capital
capital.@inProvince  province.@name
In contrast, one can specify keys and foreign keys in SQL without
worrying about their consistency with schema.
25
Cardinality constraints by keys, foreign keys
Constraints  :
province.@name
 province
capital.@inProvince  capital
capital.@inProvince  province.@name
Notation:
 ext(): the set of  elements in an XML document
 ext(.l): the set of l attribute values of all  elements

|ext(province.@name)|
= |ext(province)|
|ext(capital.@inProvince)| = |ext(capital)|
|ext(capital.@inProvince)|  |ext(province.@name)|
 |ext(capital)|  |ext(province)|
26
Cardinality constraints imposed by DTDs
DTD D: <!ELEMENT db
(province+, capital+)>
<!ELEMENT province (city*, capital)>
Variables:
 Xprovince: the number of province elements under the root
 Xcapital: the number of capital subelements of the root
 Ycapital: the number of capital subelements of province’s

Xprovince  1, Xcapital  1
|ext(province)| = Xprovince, Xprovince = Ycapital
|ext(capital)| = Xcapital + Ycapital

|ext(capital)| > |ext(province)|
27
The interaction
Contradiction:
 From the constraints  : |ext(capital)| 
|ext(province)|
 From the DTD D:
|ext(province)|
|ext(capital)| >
Thus there exists NO XML document that both conforms to D and
satisfies .
db
province
@name
city
province
...
capital
“Limburg”
capital
capital
“Hasselt”
@inProvince
“Limburg”
“others” @inProvince “Hasselt”
“Limburg”
28
Consistency analysis [PODS’01, 02]
 Trivial for relational databases: given any schema and keys,
foreign keys, one can always find a nonempty instance of the
schema satisfying the constraints.
 Hard for XML: XML specifications may not be consistent!
– Both DTDs and constraints impose cardinality constraints
– The interaction between these two classes of cardinality
constraints is rather complicated.
29
Consistency analysis of XML constraints
Theorem: The consistency problem is
 undecidable for multi-attribute absolute keys and foreign keys;
 NP-complete for unary absolute keys and foreign keys, even for
primary keys (primary: at most one key for each element type);
 in NEXPTIME for primary multi-attribute absolute keys and
unary foreign keys
 in NEXPTIME and PSPACE-hard for unary absolute regular
keys and foreign keys (target path: /, where  is a regular path
expression and  an element type; key paths: attributes)
 undecidable for relative keys and foreign keys, even when all
the constraints are unary and primary.
As opposed to the trivial analysis of the relational counterpart.
30
Some tractable cases
 Restrictions on constraints.
Theorem: For multi-attribute relative keys only, the consistency
problem is in linear time for arbitrary DTDs.
Recall relative keys: country (province.@name  province)
In contrast, due to the existence and uniqueness condition:
Theorem: It is intractable for unary keys alone in XML Schema.
 Restrictions on DTDs:
Theorem: When DTD is fixed, the consistency problem is in PTIME
for absolute unary keys and foreign keys.
In practice, DTD is designed at one time, but constraints are written
in stages: constraints are incrementally added.
31
Implication analysis [PODS’00, 01, 02, DBPL’01]
Given D: a DTD
: a set of constraints expressed in C
: a property (a constraint of C)
Implication (C ): Is it the case that for any XML document, if it
conforms to D and satisfies , then it must satisfy ?
C: a constraint language
The need for studying implication:
 data integration: constraints checking at virtual views
 optimization of XML queries and XML relational storage
 design theory for XML specifications: normalization
32
Some complexity results for implication analysis
Theorem: The implication problem is

undecidable for multi-attribute absolute keys and foreign keys,
and for unary relative keys and foreign keys;
 PSPACE-hard for unary regular absolute keys and foreign keys;
 coNP-complete for unary absolute keys and foreign keys.
 coNP-hard for XML-Schema unary keys
 in linear time for absolute multi-attribute keys;
 in PTIME for arbitrary absolute keys and foreign keys when the
DTD is fixed, and
 in PTIME for relative path keys in the absence of DTDs
The analysis of XML constraints is far more intricate than its
relational counterpart
33
Applications
 Application of XML constraints, and open problems
– Constraint propagation
– Schema-directed XML integration
– Normal form
– Query rewriting/optimization
– Update processing
– Data cleaning
– ...
34
XML shredding: relational storage of XML data
Web
XML
XML keys
XML
XML shredding
DB1
propagation
DB2
relational FDs
XML shredding:
 mapping XML data to relations
 relational design: normalization
– optimal relational storage of XML data
– semantic connection: query/update optimization
35
Example: XML constraints
 (//book,
{isbn})
-- isbn is an (absolute) key of book
 (//book,
(chapter, {number}) -- number is a key of chapter
relative to book
 (//book, (title, { })) -- each book has a unique title
db
book
isbn
“XML”
“1”
title
book
chapter
chapter
number section
number text
title
DTD
number section
“6”
number
book
book
isbn
chapter
chapter
“XML” number title
number
title
“1” XPath
36
“10”
Mapping from XML to a predefined relation
Predefined RDB: chapter(bookTitle, chapterNum, chapterTitle)
 Mapping: for each book, extract its title, and the numbers and
titles of all its chapters
 Predefined relational key: (bookTitle, chapterNum)
Can the XML data be mapped to the RDB without violating the key?
db
book
isbn
“XML”
“1”
title
book
chapter
chapter
number section
number text
title
DTD
number section
“6”
number
book
book
isbn
title
chapter
chapter
“XML” number title number
37
“1” XPath “10”
A safe mapping
Now change the relational schema to
RDB: chapter(isbn, chapterNum, chapterTitle)
The relation can be populated without any violation. Why?
The relational key (isbn, chapterNum) for chapter is implied
(entailed) by the keys on the original XML data:
(//book,
{isbn}),
(//book,
(chapter, {number}),
(//book, (title, { }))
db
book
isbn
“XML”
“1”
title
book
chapter
chapter
number section
number text
title
DTD
number section
“6”
number
book
book
isbn
title
chapter
chapter
“XML” number title number
38
“1” XPath “10”
Constraint Propagation [ICDE’03]
 Input:
– a set K of XML keys (context and target path: a fragment of
XPath, key paths: attributes)
– a predefined relational schema S,
– a mapping f from XML to S (XPath, projection, join, union)
– and a relational functional dependency FD over S
 Output:
is the FD propagated from K via f? I.e., does FD hold
over the DB f(T) for any XML document T that satisfies K?
Theorem: The constraint propagation problem is in PTIME.
 Checking the consistency of a predefined relational schema for
storing XML data
 XML schema/DTD is not required – K is the only semantics
39
Deriving relational schema for storing XML
One wants to find a “good” relational schema to store:
chapter(isbn, bookTitle, author, chapterNum, chapterTitle)
What is a good schema? In normal form: BCNF, 3NF, …
 Prevent update anomaly (the relational theory)
 Efficient storage, query optimization …
But how to find a normalized design? db
book
isbn
“XML”
“1”
title
book
chapter
chapter
number section
number text
title
DTD
number section
“6”
number
book
book
isbn
title
chapter
chapter
“XML” number title number
40
“1” XPath “10”
Constraint propagation and normalization
From the given XML keys:
(//book,
{isbn}),
(//book, (chapter, {number}),
(//book, (title, { }))
one can derive functional dependencies:
isbn  bookTitle,
isbn, chapterNum  chapterTitle
Normalize the relation by using these functional dependencies:
chapter(isbn, bookTitle, author, chapterNum, chapterTitle)
book(isbn, bookTitle),
chapter(isbn, chapterNum, chapterTitle),
author(isbn, author)
The new schema is in BCNF!
41
Computing minimum cover of propagated FDs
 Input: a set K of XML keys, and a mapping f from XML to a
universal schema U
 Output: a minimum cover F of all the functional dependencies
(FDs) propagated from the XML keys K via f
– F is a cover (a set of FDs): any FD propagated from K via f is
implied by F
– F is minimum: F contains no redundant FDs, i.e., any FD in
F is not entailed by other FDs in F.
Theorem: There is a PTIME algorithm for computing a minimum
cover of propagated FDs.
Normalize relational schema for storing/querying XML data!
42
Research issues
For general constraints/mapping languages: undecidable
 if the mapping language is relationally complete (selection,
projection, join, union, difference), even for XML keys alone
 if both XML keys and foreign keys are considered, even for the
identity “transformation”
Open:
 To identify (a) practical mapping languages and (b) practical
XML constraints that allow efficient constraint propagation
 Constraint propagation from relations to XML
– Information preserving (lossless) data exchange
– Query/update rewriting/optimization
– Overcoming incompleteness of source data (foreign keys)
43
XML publishing/integration
Web
DTD
XML
constraints
XML
Q: XML view
DB1
DB2
All members of a community (or industry) agree on a schema and
exchange data w.r.t. the schema: e-commerce, health-care, ...
Schema-directed XML Publishing/Integration:
 mapping data from traditional database to XML
 satisfying the predefined DTD and constraints
44
Schema-directed integration [SIGMOD’03]
DB
DTD
integration
DB
DB
constraints
XML view
multiple, distributed sources
Schema-directed: XML view conforming to a schema (D, )
– D: a DTD
– : a set of XML constraints (relative keys, foreign keys)
 Attribute Integration Grammar (AIG)
DTD-directed view definition: recursive, nondeterministic
Inherited and synthesized attributes
Constraint compilation: automatically captures integrity
constraints and DTD in a uniform framework
45
XML normal forms
 Extensions of (nested) relational normal forms, via XML FDs
– M. Arenas and L. Libkin. A Normal Form for XML Documents,
[PODS 02]. XNFs, decomposition algorithms, complexity, …
– M. Vincent, J. Liu and C. Liu. Strong functional dependencies and
their application to normal forms in XML. [TODS 29(3), 2004]
– X. Wu, T.W. Ling, S. Lee, M. Lee, G. Dobbie. NF-SS: A Normal
Form for Semistructured Schema. [ER (Workshops) 2001]
 Research issues
– Implication analysis: more intriguing than relational FDs
– Relative functional dependencies: hierarchical nature of XML
– “Right” normal form: XML data is typically stored in RDBMS
• redundancy often helps, e.g., performance and reliability
• XML data is often “static”: update anomalies?
46
Run-time analysis: incremental constraint checking
Input: XML tree T, constraints , update ∆T, where T satisfies 
Question: does (T + ∆T) satisfy ?
 ∆X . Code generator: incremental checking. Lucent applications
M. Benedikt, G. Brun, J. Gibson, R. Kuss and A. Ng. Automated
update management for XML integrity constraints. [PLANX’02]
 Application of incremental techniques for attribute grammar
M. Abrao, B. Bouchou, M. Alves, D. Laurent, M. Musicante.
Incremental Constraint Checking for XML Documents [XSym’04]
Research issues:
 Complexity of incremental constraint checking
 XML editors: broken link detection and repair
 Incremental checking techniques for XML data stored in RDBMS
47
Query rewriting and optimization
Query translation from XQuery to SQL: XML data stored in RDBMS
– encode XIGs and XQuery in relational queries and constraints
– extensions of chase and backchase
A. Deustch and V. Tannen
– Reformulation of XML Queries and Constraints [ICDT’03]
– MARS: A System for Publishing XML from Mixed and Redundant
Storage [VLDB’03]
R. Krishnamurthy, R. Kaushik, J. Naughton. Efficient XML-to-SQL
Query Translation: Where to Add the Intelligence? [VLDB 2004]
Research issues:
 Rewriting queries over (recursive security) views of XML data
 Query optimization for (compressed) XML data in native store
48
Data cleaning
Input: XML tree T, constraints , DTD D
Question: if T does not satisfy D + , find a repair T’ such that (a) T’
satisfies D + , and (b) the distance between T and T’ is minimal
(update operations: insert, delete, modify)
 G. Flesca, F. Furfaro, S. Greco, E. Zumpano. Repairs and Consistent
Answers for XML Data with Functional Dependencies [XSym’03]
Research issues:
 Effective techniques for repairing integrated XML data: conflicts
and inconsistencies may emerge as violations of constraints.
– Various constraint languages,
– XML schema
 Automated tools for repairing Web pages: broken links
49
Summary
 Specification of XML constraints:
– absolute vs. relative, path constraints: XML data is
hierarchical and semi-structured
– mild extensions of relational constraints are not sufficient
 Consistency and implication analysis of XML constraints
– DTDs interact with XML constraints
– far more intricate than their relational counterparts
 Applications of XML constraints
– XML storage, query, update, integration, cleaning, …
– many practical issues remain to be explored
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