Complexity and Enumeration in Models of Genome Rearrangement

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, Medvedev, & Stoye, J. Comput. Biol. 2010) is $\mathrm{\#}\mathsf{\text{P}}$-complete under polynomial-time Turing reductions. Next, we show that in the Single Cut or Join model (Feijao & Meidanis, IEEE ACM Trans. Comp. Biol. Bioinf. 2011), the problem of enumerating all medians ($\mathrm{\#}$Median) is logspace-computable ($\mathsf{\text{FL}}$), improving upon the previous polynomial-time ($\mathsf{\text{FP}}$) bound of Miklós & Smith (RECOMB 2015).