Before revision:  We further analyze the problem in more practical way and consider the variation where a certain number of prefix reversals are forced to happen in the sorting process. Here we achieve an improved approximation ratio of (3-\frac{3r{b(\pi)+r}), where r is the }  number of prefix reversals that must happen in the sorting, when possible, and b(\pi)\geq 2r is the number of breakpoints in the given permutation.
After revision:  We further analyze the problem in more practical way and {b(\pi)+r}), where r is the } number of prefix reversals that must happen in the sorting, when possible, and b(\pi)\geq 2r is the number of breakpoints in the given permutation.