AVOIDING UNNECESSARY ORDERING OPERATIONS IN XPATH

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AVOIDING UNNECESSARY ORDERING OPERATIONS IN XPATH

• Jan Hidders
• Philippe Michiels

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Problem

• XPath semantics require the result of a query to
  be in doc-order and contain no duplicate nodes
• Many implementations achieve this by explicitly
  ordering intermediate results or sacrificing
  correctness for efficiency
• In case of large input documents, this approach
  impacts the performance
• Motivation Galax

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XPath implementation

• Explicit sorting and duplicate elimination after
  each step by inserting distinct-docorder (ddo)
  operations in query plan

• Semantics of implementation without ddos
  sloppy semantics

• Example /descendant-or-selfa/childb

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XPath Properties

• We need to identify several properties of path
  expressions that assist us in determining whether
  their sloppy semantics are equal to their formal
  semantics
• Two main properties
• ord (result always in order)
• nodup (result never contains duplicate nodes)
• Additional properties necessary, e.g.
• gen (all nodes in result belong to same
  generation)
• max1 (result contains at most one node)
• unrel (result contains no related nodes)
• lin (all nodes in result are anc-desc related)

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Rules for the Inference of Path Properties

• We define a set of inference rules for the
  deduction of the ord and nodup properties
• For example

The gen property is preserved by de child,
parent, foll-sibl, prec-sibl axes.
If the gen property holds, then the ord property
is preserved by the parent axis.
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Deterministic Automata

• The rules allow us to construct a deterministic
  automaton that verifies whether the sloppy
  semantics of XPath queries have the nodup/ord
  property
• For brevity, we only discuss the automaton that
  checks for the ord-property

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Aord Automaton
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Example (1)
/desc-or-selfa/childb/foll-siblb/parenta
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Example (2)
/ ? 1
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Example (3)
/ ? 1
desc-or-selfa ?1,6
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Example (4)
/ ? 1
desc-or-selfa ? 1,6
childb ? 2,3,4,5,9,10,7,8
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Example (5)
/ ? 1
desc-or-selfa ? 1,6
childb ? 2,3,4,5,9,10,7,8
foll-siblb ? 3,4,5,4,5,5,10,8
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Example (6)
/ ? 1
desc-or-selfa ? 1,6
childb ? 2,3,4,5,9,10,7,8
foll-siblb ? 3,4,5,4,5,5,10,8
Parenta ? 1,1,1,1,1,1,1,6
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Soundness Completeness

• For the XPath-fragment
• P A P/A
• A parentchildancestordescendant...
• the set of inference rules is sound complete
  for the ord and nodup properties

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Conclusions

• We can derive whether a query evaluated by the
  sloppy semantics, returns a result that is free
  from duplicates and/or in document order
• We can use this knowledge to
• eliminate unnecessary ddo-operations in the query
  plan
• rewrite the query to avoid generation of
  unnecessary ordering operations

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Further Work

• Our automaton does not consider ddo-operations in
  de query plan. The automaton does not define
  transitions for ddo-operations
• For example, if after every step in the
  expression child/foll-sibl/child, a
  sorting operation is performed, there is no need
  for sorting at the end of the expression. But our
  algorithm is incapable of deducing this.

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Further Work (2)

• How to decide where to sort?

Example /descendant-or-selfa/childb/parenta