Type Indexing in XML Database

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Type Indexing in XML Database
Akhilesh Shirbhate (02329014)
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Indexing in XML Databases

• Structured or semi-structured semantic tag
  system.
• Real useful data has some semantic meaning.
• Huge size of XML documents in its repository.
• Providing answers efficiently for queries is very
  challenging.
• We need indices !!!
• The indexing for tree structured XML database is
  still an active research area.

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Terminology

• Judgements in type system
• Type rules in type system
• Type equivalence
• Subtyping

• DTD
• XML Schema
• XQuery
• Type
• Typed Language

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Subtyping Proposals for XML

• XML Schema
• XQuery
• Xduce
• Tindex

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XML Schema

• Simple and Complex Types
• Simple type gtgt value space, lexical space, set
  of facets
• Facets gtgt fundamental, restrictive
• Complex types gtgt order constraint, occurrence
  constraint
• Model groups gtgt particles held together.
• Supports Restriction subtyping and Extention
  subtyping.

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Xquery

• Expression rich
• path expr (based on XPath)
• element constructor
• FLWR expr (for, let, where, return)
• data type modification and comparing (cast)
• Kleene operators supported.
• Can compute joins !!

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Xduce

• Functional language
• Provides
• Subtyping algorithm for regular expression types.
• Type inference algorithm for regular expression
  pattern matching.
• Type definition
• T () Empty sequence
• T X Type name
• T l T Label
• T T , T Concatenation
• T T T Union

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Xduce (continued)

• Xduce types are equvalent to XQuery types

DEFINE TYPE l1 ELEMENT person ELEMENT name
xsstring, ELEMENT tel xsstring
type l1 person name String, Xtelsta
r type Xtelstar telString,Xtelstar ()
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Xduce internal form

• Internal type expression T is
• T ø Empty set
• T í Leaf
• T ß Internal type
• T T T Union
• T l (X , X) Label
• Type equivalence
• T ø T
• T T T
• ( T U ) R T ( U R )
• T U U T
• T U T R if U R

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Tindex

• Has its roots in theorem proving systems and
  XDuce.
• Terminology
• term, variable (), clause, multiliteral clause
• Unification Problem
• The unification problem consists of selecting all
  terms l in S such that there exists a
  substitution µ that satisfies lµ tµ. For
  instance, the terms f (a, b) and f (, ) are
  both unifiable with the term f (a, ).

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Problem Specified !!!

• Term Indexing problem
• Given a set S (called the set of indexed terms),
  a binary relation R over terms (called the
  retrieval condition), and a term t (called the
  query term), identify the subset M of S
  consisting of all terms l such that R(l,t) hold
  true.
• Type Indexing problem
• Given a set S (called the set of indexed types),
  a binary relation R over types (called the
  retrieval condition), and a type t (called the
  query type), identify the subset M of S
  consisting of all types l such that R(l,t) hold
  true.

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Supertype selection problem

• Supertype selection problem
• Given a set S of types, and a query type t,
  identify the subset M of S consisting of all
  types l such that t lt l
• Solution is easy !!! Put unification as retrival
  contidition in multiterm indexing problem.
• To get absolute set of supertypes, we need to
  make a second sequencial pass over the set
  retrned by above procedure.

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Example of need for second pass
DFFINE TYPE l ELEMENT person ELEMENT name
xsstring ELEMENT tel xsstring person(
X1, X0) where M(X0) í M(X1) name(X2,
X3) M(X2) ß M(X3) tel (X2, X3) X0 l
person ( name ( ß, tel ( ß, ) í ) , í )
Similarly, l1 person ( name ( ß, ) tel (
ß, í ) , í ) l2 person ( name ( ß, ) tel (
( ß, ) í , í )
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Tindex construction
DEFINE TYPE t1 ELEMENT author ELEMENT name
xsstring, ELEMENT email xsstring
DEFINE TYPE t2 ELEMENT author
ELEMENT name xsstring, ELEMENT email
xsstring ELEMENT tel csstring
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Conclusion

• XML data gt Repositories gt XML database gt Query
  language gt Indexing gt Content/Structure gt XML
  Schema gt Tindex/XDuce
• Problems gt Type inference , subtyping, retrival
  and unification.
• Tindex solves the problem elegantly using theory
  from the domain of theorem proving and
  datastructures like trie.
• Further research is active because the indexing
  needs of XML databases differ from those of
  relational databases due to semi-structuredness
  of XML documents.