Normalization Theory for XML

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Normalization Theory for XML

• Murali Mani
• Oct 17, 2003

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Why Normalization?
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How to study normalization?

• How do we specify FDs, MVDs?
• What are normalization steps?
• Different Normal Forms.

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XML Schema Structural Spec

• G (N, T, P, S)
• N Book, Author, Publisher, PCDATA
• T book, author, publisher, pcdata
• S Book
• Book ? book (Author , Publisher)
• Author ? author (PCDATA)
• Publisher ? publisher (_at_nameString)
• PCDATA ? pcdata (?)

Regular Tree Grammar Every production rule is of
the form A ? a X A ? N, a ? T, X is a regular
expression over N
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XML Schema Constraint Spec
(Library, Person, lt_at_namegt) (Library, Book,
lt_at_ISBNgt) (Library, Paper, lt_at_titlegt) (Person,
Review, lt_at_articlegt)
_at_articleIDREF references (Book Paper)
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Unnesting for XML Proposal 1
Person
The following FD holds for this
instance article, rating ? name
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Unnesting for XML Proposal 2
for p in //person for name in p//_at_name for
paper in p//_at_PID for article in
p//_at_article for article in p//_at_rating return
ltpersongt ltnamegtnamelt/namegt
ltPIDgtpaperlt/PIDgt ltarticlegtarticlelt/article
gt ltratinggtratinglt/ratinggt lt/persongt
Person
The following FD does not hold for this
instance article, rating ? name
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Example
N Root, Library, Book, Author T root,
library, book, author S Root Root ? root
(Library ) Library ? library (_at_lname, _at_address,
Book) Book ? book (_at_title, _at_loc, Author
) Author ? author (_at_aname, _at_age)

• Key constraints
• (Root, Library, lt_at_lnamegt)
• (Root, Book, lt_at_titlegt)
• (Book, Author, lt_at_anamegt)
• FDs
• (Root, Book, parentlibrary/_at_lname ? _at_loc)
• (Root, Author, _at_aname ? _at_age)

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Properties of FDs

• For any 2 types X, Y, the FD (X, Y, p ? y) is
  true, where
• p is a path expression producing 1/more
  descendant elements of Y
• Eg (X, Book, author ? book)
• For any two types X, Y, the FD (X, Y, y ? a) is
  true, where
• a is an attribute or element that can occur only
  once for a given y
• Eg (X, Book, book ? _at_title)
• Eg (X, Book, book ? parentlibrary/_at_address)
• Eg (X, Book, book ? parentlibrary)

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Properties of FDs (contd)

• To prove For any FD, (X, Y, S ? a)
• All path expressions in S end only in attributes.

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Normalization Step 1

• For a FD of the form (X, Y, S ? a)
• If ? Z such that (X, Z, S) is a key constraint
• Move a to be child of Z

(Root, Book, parentlibrary/_at_lname ? _at_loc)
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(No Transcript)
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Normalization Step 2

• For a FD of the form (X, Y, S ? a)
• If ? ? Z such that (X, Z, S) is a key constraint
• Create new type Z with (X, Z, S) as key
• Move a to be child of Z

(Root, Author, _at_aname ? _at_age)
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• Key constraints
• (Root, Library, lt_at_lnamegt)
• (Root, Book, lt_at_titlegt)
• (Book, Author, lt_at_anamegt)
• (Root, Author1, lt_at_anamegt)

• Foreign Key constraints
• (Book, Author, lt_at_anamegt) references
• (Root, Author1, lt_at_anamegt)

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Conclusions and Future Work

• Studied 2 ways of unnesting XML documents
• Defined functional dependencies
• Studied normalization Steps
• Improving the goodness of normalized XML schemas.
• Current restriction path expressions cannot
  navigate IDREF/(S)
• Inference of FDs and MVDs