# Assignment problem with symmetric matrix

I came across a problem which I think can be reduced to the assignment problem/Hungarian algorithm.

We have matrix $$A$$ and matrix $$B$$ which are both $$n\times n$$ symmetric matrices. We can rearrange $$B$$ in the following manner: column $$i$$ can be swapped with column $$j$$ provided that next, row $$i$$ is swapped with row $$j$$. This preserves the symmetry of $$B$$.

The problem statement is to find a rearrange of $$B$$ in this manner which minimizes the Frobenius norm of $$A-B$$.

Any guidance on an approach would be greatly appreciated. Thank you very much in advance.