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.
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?
> Biostatistics Consulting Center
>William D. Shannon, Ph.D.
>Associate Professor of Biostatistics in Medicine
>Division of General Medical Sciences and Biostatistics
>Washington University School of Medicine
>Campus Box 8005, 660 S. Euclid
>St. Louis, MO 63110
>e-mail: [log in to unmask]
>web page: http://ilya.wustl.edu/~shannon