When can a link be obtained from another using crossing exchanges and smoothings

Let $L$ be a fixed link. Given a link diagram $D$, is there a sequence of crossing exchanges and smoothings on $D$ that yields a diagram of $L$ We approach this problem from the computational complexity point of view. It follows from work by Endo, Itoh, and Taniyama that if $L$ is a prime link with crossing number at most five, then there is an algorithm that answers this question in polynomial time. We show that the same holds for all torus $T_{2,m}$ and all twist knots.Non UBCUnreviewedAuthor affiliation: Universidad Autónoma de San Luis Potosí InicioOthe