XML Constraints: Specification, Analysis, and Applications

1
XML Constraints Specification, Analysis, and
Applications

• Wenfei Fan
• School of Informatics, University of Edinburgh
• Network Data and Services Research, Bell
  Laboratories

2
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 . . .

3
Introduction to XML specificaiton

• XML Specification
• types
• integrity constraints
• the need for XML constraints

4
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
• _at_attributes _at_name, _at_inProvince, carrying text
• text nodes, e.g., Hasselt

5
XML specification DTD (type)

• Production constrains the subelement list of
  each element lt!ELEMENT db (province,
  capital)gt
• lt!ELEMENT province (city, capital)gt
• Attributes uniquely identified by name for each
  element, unordered
• province _at_name, capital _at_inProvince

6
XML specification integrity constraints

• Keys and foreign keys (vs. relational
  constraints)
• key the value of a _at_name uniquely identifies a
  province
• province._at_name ? province
• capital._at_inProvince ? capital
• FK _at_inProvince of a capital references _at_name of
  a province
• capital._at_inProvince ? province._at_name

7
XML specification

• A type (DTD) D
• A set of integrity constraints, ?
• Example
• DTD D structure of the document, vs. types in a
  PL
• lt!ELEMENT db (province, capital)gt
• lt!ELEMENT province (city, capital)gt
• province._at_name, capital._at_inProvince
• Constraints ? defined in terms of data values
  across elements
• province._at_name ? province
• capital._at_inProvince ? capital
• capital._at_inProvince ? province._at_name

8
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,

9
Data exchange on the Web XML publishing

• 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

Web
XML
XML
Q XML view
DB1
DB2
10
Data exchange on the Web XML shredding

• 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

Web
XML
XML
XML keys
XML shredding
propagation
DB1
DB2
relational FDs
11
XML constraints

• Specification of XML constraints
• keys, foreign keys, FDs
• absolute vs. relative constraints

12
absolute constraints

• Absolute keys and foreign keys are to hold on the
  entire document.
• province._at_name ? province
• capital._at_inProvince ? capital
• capital._at_inProvince ? province._at_name
• Extensions of relational counterparts

13
Absolute keys and foreign keys PODS00, 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 ? ?1X ?? ??2Y, and a key ?
  ?2Y ? ? ??2 .
• A document satisfies the FK iff it satisfies the
  key and
• ? x ? ext(??1 ) ? y ? ext(??2 ) (xX yY)
• ?, ?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.

14
Relative constraints WWW01, PODS02

• An XML tree specifies countries, provinces,
  province capitals.
• What is a key for a province?
• What does _at_inProvince of a capital reference?

db
...
country
country
...
...
province
capital
capital
province
_at_name
_at_name
Holland
Belgium
capital
_at_name
_at_name
capital
_at_inProvince
Hasselt
_at_inProvince
Maastricht
Limburg
Limburg
Limburg
Limburg
_at_inProvince
Hasselt
_at_inProvince
Hasselt
Limburg
Limburg
15
Examples of relative constraints

• Relative constraints on a subdocument rooted at
  a country
• key country (province._at_name ?
  province)
• country (capital._at_inProvince ? capital)
• FK country (capital._at_inProvince ?
  province._at_name)
• Absolute on the entire document country._at_name
  ? country

db
...
country
country
...
...
province
capital
capital
province
_at_name
_at_name
Belgium
Holland
capital
_at_name
Hasselt
capital
_at_name
_at_inProvince
_at_inProvince
Maastricht
Limburg
Limburg
Limburg
Limburg
_at_inProvince
Hasselt
_at_inProvince
Hasselt
Limburg
Limburg
16
Relative keys and foreign keys

• key ??(??1X ? ??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) ??( ?1X ?? ??2Y ) and a key
  ?( ?2Y ? ??2) .
• A document satisfies the FK iff it satisfies the
  key and
• ? c ? ext(?) ? y ? ext(?1) (( y ?? c) ?
• ? z ? ext(??2 ) ((z ?? c) ? yX zY
  ))
• 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.

17
Relative vs. Absolute

• Absolute constraints are a special case of
  relative ones
• country._at_name ? country ? db ( country._at_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._at_name ? province)
• country (capital._at_inProvince ? capital)
• country (capital._at_inProvince ?
  province._at_name)
• country._at_name ? country
• Together they specify constraints on the entire
  document
• Beyond relational constraints important for
  hierarchically structured data XML, scientific
  databases, biomedical data, ...

18
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

name
name
_at_id
_at_id
firstName
lastName
19
Absolute path constraints WWW01

• 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, //_at_id) --
  multiple keys
• (//., _at_id)
  -- capturing ID attributes in DTDs

20
Relative path constraints WWW01

• 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, _at_capital))
• (//country, _at_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

21
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, P1, . . ., Pk ) ?? (S,
  S1, . . ., Sk )
• (S, 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

22
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, PODS02
• 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, KRDB01)

23
Constraint analysis

• Analysis of XML constraints
• Consistency analysis
• Implication analysis
• Absolute, relative, path-expression constraints

24
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

25
An inconsistent specification

• The specification with D and ? is inconsistent!
• DTD D
• lt!ELEMENT db (province, capital)gt
• lt!ELEMENT province (city, capital)gt
• province._at_name, capital._at_inProvince
• Constraints ?
• province._at_name ? province
• capital._at_inProvince ? capital
• capital._at_inProvince ? province._at_name
• In contrast, one can specify keys and foreign
  keys in SQL without worrying about their
  consistency with schema.

26
Cardinality constraints by keys, foreign keys

• Constraints ?
• province._at_name ? province
• capital._at_inProvince ? capital
• capital._at_inProvince ? province._at_name
• Notation
• ext(?) the set of ? elements in an XML document
• ext(?.l) the set of l attribute values of all ?
  elements
• ?
• ext(province._at_name)
  ext(province)
• ext(capital._at_inProvince) ext(capital)
• ext(capital._at_inProvince) ?
  ext(province._at_name)
• ? ext(capital) ? ext(province)

27
Cardinality constraints imposed by DTDs

• DTD D lt!ELEMENT db (province, capital)gt
• lt!ELEMENT province (city,
  capital)gt
• 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
  provinces
• ?
• Xprovince ? 1, Xcapital ? 1
• ext(province) Xprovince,
  Xprovince Ycapital
• ext(capital) Xcapital Ycapital
• ?
• ext(capital) gt ext(province)

28
The interaction

• Contradiction
• From the constraints ? ext(capital) ?
  ext(province)
• From the DTD D ext(capital) gt
  ext(province)
• Thus there exists NO XML document that both
  conforms to D and satisfies ?.

29
Consistency analysis PODS01, 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.

30
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.

31
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._at_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.

32
Implication analysis PODS00, 01, 02, DBPL01

• 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

33
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

34
Applications

• Application of XML constraints, and open problems
• Constraint propagation
• Schema-directed XML integration
• Normal form
• Query rewriting/optimization
• Update processing
• Data cleaning
• . . .

35
XML shredding relational storage of XML data

• XML shredding
• mapping XML data to relations
• relational design normalization
• optimal relational storage of XML data
• semantic connection query/update optimization

Web
XML
XML
XML keys
XML shredding
propagation
DB1
DB2
relational FDs
36
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

chapter
chapter
37
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?

38
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, ))

39
Constraint Propagation ICDE03

• 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

40
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?

41
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!

42
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!

43
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)

44
XML publishing/integration

• 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

Web
XML
XML
Q XML view
DB1
DB2
45
Schema-directed integration SIGMOD03
DTD
DB
DB
integration
DB
constraints
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

46
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?

47
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. PLANX02
• Application of incremental techniques for
  attribute grammar
• M. Abrao, B. Bouchou, M. Alves, D. Laurent, M.
  Musicante. Incremental Constraint Checking for
  XML Documents XSym04
• Research issues
• Complexity of incremental constraint checking
• XML editors broken link detection and repair
• Incremental checking techniques for XML data
  stored in RDBMS

48
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
  ICDT03
• MARS A System for Publishing XML from Mixed and
  Redundant Storage VLDB03
• 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

49
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 XSym03
• 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

50
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