Complexity and enumeration in models of genome rearrangement

Abstract

In this paper, we examine the computational complexity of enumeration in certain genome rearrangement models. We first show that the Pairwise Rearrangement problem in the Single Cut-and-Join model (Bergeron et al., 2010 [8]) is $\#\text{P}$-complete under polynomial-time Turing reductions. Next, we show that in the Single Cut or Join model (Feijão and Meidanis, 2011 [21]), the problem of enumerating all medians (

) is logspace-computable ($\text{FL}$), improving upon the previous polynomial-time ($\text{FP}$) bound of Miklós & Smith [41].