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Re: XPath filter 2.0

From: merlin <merlin@baltimore.ie>
Date: Thu, 06 Jun 2002 12:22:47 +0100
To: Christian Geuer-Pollmann <geuer-pollmann@nue.et-inf.uni-siegen.de>
Cc: w3c-ietf-xmldsig@w3.org
Message-Id: <20020606112247.33DB34432D@yog-sothoth.ie.baltimore.com>

r/geuer-pollmann@nue.et-inf.uni-siegen.de/2002.06.06/10:29:55
>>     * Implementations SHOULD note that an efficient realization
>>       of this transform will not compute a node set at each
>>       point in this transform, but instead make a list of
>>       the operations and the XPath-selected nodes, and then
>>       iterate through the input document once, in document
>>       order, constructing a filtering node set N based upon
>>       the operations and selected nodes.
>>   .......
>>   . Efficiency is as with the current spec. Basically this
>>     fixes union.
>
>Does this mean that based on the operations, you make some tree-labeling 
>;-)) and then you make one tree-traversal to output the selected nodes? 

Yes, but this is the exact algorithm that implementations
of the _current_ XPath Filter 2.0 transform _should_ use
if a sequence of the current XPath Filter 2.0 transforms
precedes c14n. This formulation of the filter simply makes
it easier to express in terms of SHOULD language.

>Sounds cool, in that case, the efficiency would be much better then the 
>current results of v2.0. What kind of algorithm do you use for
>
> - make a list of operations and selected nodes,
> - decide based on this data which nodes are the result.

If you're asking for a normative algorithm for the general
case, then I would have to think for a while. Restricting
myself somewhat:

First, let's characterize a sequence of filters:
  Filter ::= (INTERSECT | SUBTRACT | UNION)+
  
You will observe that adjacent SUBTRACT and INTERSECT
operations can be idempotently reordered, and that
adjacent operations of the same type can be computationally
merged. However, I would expect that type of thing to be
done in the XPath expressions so I will ignore this.

Restricting myself to the following production, which captures
all _common_ (in my opinion) use cases:
  SimpleFilter ::= A:UNION* (B:INTERSECT | C:SUBTRACT)* D:UNION*

Iterate over the document.
  (define (include-node) ;; whether or not to include a node
    (cond ;; returns the first match
      ((encountered-any D) t)
        ;; if you've encountered a node in a trailing union
      ((encountered-any C) nil)
        ;; not if you've encountered a subtraction node
      ((null B) t)
        ;; if there are no intersect operations
      ((encountered-all B) t)
        ;; if you've encountered a node in each intersect node set
      (t nil))) ;; not otherwise

Note that encountered-any returns nil if its parameter is an
empty list of node sets, but encountered-all is true in this
case. We can therefore express this concisely:
  (define (include-node)
    (or (encountered-any D)
      (and (not (encountered-any C)) (encountered-all B))))

You can implement encountered-foo and therefore include-node
strictly in terms of node labeling, a stack and iteration.
Obviously you must also consider the input node set.

Going from this to a fully general solution is fairly
straightforward. Observe that UNIONs are subject to ALL
subsequent INTERSECT and SUBTRACT operations, but no preceding
ones, and that the entire filter is equivalent to:
  UNION/ Filter

I can then say that a node is included if I have encountered
a node in ANY ( UNION operation AND NOT ANY SUBSEQUENT SUBTRACT
operation AND ALL SUBSEQUENT INTERSECT operations ).

Work done to compute this is proportional to the number of
filters but only done at a labeled node.

Merlin

>Christian
>
>
>
>
>--On Donnerstag, 6. Juni 2002 01:09 +0100 merlin <merlin@baltimore.ie> 
>wrote:
>
>>
>>
>> Hi,
>>
>> Quick summary of options:
>>
>> 1. Current Spec
>>   . This is intuitive (in my opinion) because it is based on a
>>     linear sequence of set operations.
>>   . Typical (IMHO) use cases require 2 XPath evaluations.
>>     However, increasingly complex filtering requirements incur
>>     increasing cost; an arbitrarily complex expression requires
>>     an arbitrarily large number of simple XPath expressions.
>>     However, the standard XPath filter may be more useful for
>>     these anyway.
>>   . Operation can, in most cases, be commingled with c14n for
>>     efficiency, but:
>>   . The union operator is really ugly and unintuitive.
>>
>> 2. Christian's Spec
>>   . *I* do not believe this is as intuitive; it involves labeling
>>     nodes and then traversing the document, proceeding based
>>     on node labels (e.g., omit-but-traverse).
>>   . Typical use cases require 2 XPath evaluations. Increasingly
>>     complex filtering requirements can be solved in a fixed
>>     number (2/3) of increasingly complex XPath expressions.
>>   . Operation can be commingled with c14n for effiency.
>>
>> 3. Or, we can take a variant of the current spec. I won't
>>    detail it horrendously, but basically:
>>
>>   . The XPath Filter 2.1 takes, as a parameter, a sequence
>>     of operations, each of which is characterized as a
>>     set operation (intersect, subtract, union) and an
>>     XPath expression.
>>   . Operation over an input node set is as follows:
>>     * Construct a node set N consisting of all the
>>       nodes in the input document.
>>     * Iterate through each of the operations.
>>       # Evaluate the XPath expression; the result is X.
>>       # Expand all identified nodes to include their
>>         subtrees; the result is Y.
>>       # Assign N = N op Y
>>     * Use the resulting node set N as a filter to select
>>       which nodes from the input node set will remain in the
>>       output node set, just as the XPath 1.0 filter. This is
>>       tantamount to intersection with the input node set.
>>     * Implementations SHOULD note that an efficient realization
>>       of this transform will not compute a node set at each
>>       point in this transform, but instead make a list of
>>       the operations and the XPath-selected nodes, and then
>>       iterate through the input document once, in document
>>       order, constructing a filtering node set N based upon
>>       the operations and selected nodes.
>>     * Implementations SHOULD note that iterating through the
>>       document and constructing a filtering node set N can
>>       be efficiently commingled with the canonicalization
>>       transform if canonicalization is performed immediately
>>       after this transform.
>>   . With this formulation, intersection and subtraction
>>     are IDENTICAL to the existing spec, with the only
>>     change being that you can put them in one transform
>>     or many.
>>   . Union is, however, much improved (in my opinion). You
>>     can only use it to include nodes that would be
>>     removed by a previous operation in the same transform.
>>     As a result, the output node set will only include
>>     nodes from the input node set.
>>   . Efficiency is as with the current spec. Basically this
>>     fixes union.
>>
>> I write this a while ago; thought I'd send it rather
>> than delete it. It's probably wasteful to propose yet
>> another option.
>>
>> Merlin
>
Received on Thursday, 6 June 2002 07:23:22 GMT

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