[R] reordering of matrix rows to maximize the sum of the diagonal

[Jonathan]

Hi r-help community,
    This question isn't so much a syntax/coding one, but here goes:

Let's say I have matrix of arbitrary dimensions and I'd like to
reorder the rows in such a way that I could maximize the sum of the
entries along the diagonal.

For example, for this 3x3 matrix:


     [,1] [,2] [,3]
[1,]    3    4   13
[2,]    9    1    2
[3,]    2   11    1

rearranging the rows to maximize the sum along the diagonal would
produce this matrix:

     [,1] [,2] [,3]
[1,]    9    1    2
[2,]    2   11    1
[3,]    3    4   13


I've been experimenting with some scripts of my own, but I figured I'd
ask if one of you R-ninjas might know of an existing function (or
algorithm I could look up and then code) that can do this somewhat
efficiently (or even just correctly!).

Best,
Jonathan