I have been struggling with a combinatorial problem that eventually translates to the following:
Given an $n \times n$ nonnegative matrix, find a permutation of the rows that maximizes the trace.
I could compute all $n!$ permutations and find the one that maximizes the trace, but that is not computationally efficient. What is the most efficient way of accomplishing this?
If it helps, this is the same as finding $n$ entries of the matrix with no two of them in the same row or column, so that the sum of these entries is maximal.