# Weighted Sorting Algorithm

Given a permutation of $$n$$ element and for each pair of position $$i$$ and $$j$$, a non-negative integer $$c_{ij}$$ which is cost of swapping $$i$$-th element and $$j$$-th element of permutation.

Is there any polynomial or pseudo-polynomial algorithm to sort the permutation with minimum cost?

• Is this a fictional or a part of research problem? – kelalaka Oct 18 '18 at 14:11
• It is generalized form of part of a research problem. – Reza Oct 18 '18 at 19:48