uniq matrix odering

[Daniel Heiserer]

Hi,
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
exchanges.
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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"
solution.
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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