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uniq matrix odering

From: Daniel Heiserer
Subject: uniq matrix odering
Date: Wed, 29 Sep 1999 18:28:40 +0200

my question is offtopic, but I think there are enough 
math-related guys here who might have a nice idea.

Assume I have a matrix consisting only of 0 and 1 (sparse).
Size is n x m. Where n is nearly m and in  the size of maximum 10000.

Each row contains betwen 2 and 8 times "1".
Each of the colums contains between 1 and about 10 "1".

Now assume I allow to permutate row exchanges as well as column
Is there one configuration which is unique (except of some symmetries)?
What would be the criteria?
Which means for me regarding of which start-configuration I begin
I end up with the same end-configuration.
Again it is not that I have a criteria, where I look for the "best"
I look for a unique solution (except symmertry) and I want to know the
criteria for that (e.g. keep the lower left as "0" as possible,
or charge off-diagonals by its distance, ....).

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