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If your matrix can be reorganize as an Robinson matrix, you have a lot of good algorithms as I described in the manual of PermutMatrix, a software for seriation and clustering (http://www.lirmm.fr/~caraux/PermutMatrix/).
I also give some references.
For the general case, I think you have to perform every reordering if you want an exact solution.

Gilles


Le 18:18 29/06/2005, vous avez écrit:
>Mighty mathematicians we have a question.
>
>We have small matrices of integers that we need to reorder so that the sum
>of the diagonal is maximum.
>
>These matrices are relatively small (say 10x10 max) so we can brute force
>our way by performing every reordering, but would rather not.
>
>Can anyone help we biostatisticians with an algorithm or theorem?
>
>
>Bill
>---
>
>                        Biostatistics Consulting Center
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>
>William D. Shannon, Ph.D.
>
>Associate Professor of Biostatistics in Medicine
>Division of General Medical Sciences and Biostatistics
>
>Washington University School of Medicine
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