Given a symmetric correlation matrix $\in\mathbb R ^d$. I want to find a permutation of the rows/columns of the matrix to minimize the sum of the entries of the first diagonal above the main diagonal, that is $min(a_{1,2}+a_{2,3}\dots+a_{n,1})$.
If i exchange rows $n$ and $m$ i also have to exchange the columns as well to keep the symmetry.
Since going through all $d!$ possibilities is not an option, I was wondering if there is an algorithm to find a sorting of the rows/columns to find a minimizer or at least get somewhat close to a minimizing solution.