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RE: Ordered union of sequences

Subject: RE: Ordered union of sequences
From: "Michael Kay" <mike@xxxxxxxxxxxx>
Date: Thu, 8 Apr 2010 15:09:52 +0100
RE:  Ordered union of sequences
It seems to me that you first want to create (or imagine) a graph: in your
example there are arcs k->o, o->p, p->c, a->b, b->c, etc.

Then you want to look for cycles in this graph. If any cycles exist, there
is no solution to your problem.

If there are no cycles then there is a partial ordering, and you can for
example label each node with the length of the longest path leading to that
node, and then sort the nodes by this value of this label.

One way to implement this, depending on your data, might be to replace the
strings (k, o, p, c, f) with "full paths" (k, ko, kop, kopc, kopcf), then
group these full paths by the value of the last symbol in the path, then
sort the groups by the length of the longest path in the group.


Michael Kay

> -----Original Message-----
> From: Michael M|ller-Hillebrand [mailto:mmh@xxxxxxxxxxxxx]
> Sent: 08 April 2010 14:29
> To: XSL-List
> Subject:  Ordered union of sequences
> Hello experts,
> I tried hard to come up with a good subject, but maybe I
> failed. I am looking for pointers and terms that I can use
> for further research. The task at hand, which I plan to solve
> in XSLT2, is the creation of a combined master sequence of a
> number of sequences in a way so the internal order of
> sequence items (identified by their name) is preserved (and
> inconsistencies can be reported).
> There is an arbitrary number of sequences, sometimes
> containing items with the same name:
> (k, o, p, c, f)
> (d, e, f, g)
> (k, f, z, o)
> (a, b, c, d)
> I want to create a master sequence which contains every item
> once, preserving the original order.
> There are many possibilities for inconsistencies (like above
> the item "o" appears before and after "f", which should be
> detected as an inconsistency) and obviously there is more
> than one possible solution. Luckily I am only interested in
> one solution, e.g.:
> (a, b, k, o, p, c, d, e, f, z, g)
> The XSLT union operator treats sequences like unordered sets
> and only solves the problem of removing duplicates.
> BTW, the idea behind this is to create part of an XML Schema
> from evaluating document instances.
> I am thankful for any pointers,
> - Michael M|ller-Hillebrand
> --
> _______________________________________________________________
> Michael M|ller-Hillebrand: Dokumentation Technology Adobe
> Certified Expert, FrameMaker Consulting and Training,
> FrameScript, XML/XSL, Unicode Blog [de]: http://cap-studio.de/

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