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Date:	Wed, 16 Apr 2003 21:02:11 PDT
From:	Peter Skye <pskye@peterskye.com >
Reply-To:	scoug-programming@scoug.com
To:	scoug-programming@scoug.com
Subject:	SCOUG-Programming: enumerate all permutations ?

Content Type: text/plain

Steven Levine wrote:
>
> I'm actually surprised you don't already
> have this in your optimization code.

My financial optimizations run in a fundamentally different way. Each
different expression (such as "What is the seasonal impact?" or "What is
the impact of the Nikkei-to-FTSE ratio?") is first optimized
independently. Then *all* of these expressions are additively combined
with respective coefficients and the coefficients are jointly optimized.

For example, if fA() is "What is the seasonal impact?" and fB() is "What
is the impact of the Nikkei-to-FTSE ratio?", then fA() and fB() are
first independently optimized as if each is the *only* function in the
system. Once the optimal fA() and fB() are determined, then they are
additively combined as

[ C1 * fA() ] + [ C2 * fB() ]

and the coefficients C1 and C2 are jointly optimized.

There are no permutations, i.e. exotic expressions such as

fA() ^ fB()
and
fB() ^ fA()

are not considered.

> Google reports:
> http://www-or.amp.i.kyoto-u.ac.jp/members/yagiura/papers/common95-e_abst.html
> etc. for:
> enumerate all permutations algorithm

Thanks. Unfortunately it's in PostScript which I can't render here.

I did at first go to Google but was stymied by the massive number of
references, and was hoping that someone could simply suggest a "best"
algorithm. The best reference I have found so far is "Permutations by
Interchanges" by B. R. Heath (1963) which Sedgewick claims is the
fastest known, but finding Heath's paper was a chore. I have finally
located it (in TIF format!) at The Oxford University Press in England.

- Peter

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