Complexity and Enumeration in Models of Genome Rearrangement

TL;DR

The computational complexity of enumeration in certain genome rearrangement models is examined, showing that the Pairwise Rearrangement problem in the Single Cut-and-Join model is $\#\textsf{P}$-complete under polynomial-time Turing reductions.

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, Medvedev, & Stoye, J. Comput. Biol. 2010) is $\#\textsf{P}$-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 ($\#$Median) is logspace-computable ($\textsf{FL}$), improving upon the previous polynomial-time ($\textsf{FP}$) bound of Miklós & Smith (RECOMB 2015).

Figures (3)

• Figure 1: An edge-labeled genome.
• Figure 2: (i) Adjacency $X_2^hX_3^t$ is cut. (ii) Telomeres $X_1^h$ and $X_3^h$ are joined. (iii) Adjacency $X_2^hX_3^t$ is cut, and resulting telomere $X_2^h$ is joined with $X_1^h$. (iv) Adjacencies $X_1^tX_2^t$ and $X_2^hX_3^t$ are replaced with $X_1^tX_2^h$ and $X_2^tX_3^t$.
• Figure 3: An adjacency graph $A(G_1,G_2)$ is shown in the middle, with genomes $G_1$ and $G_2$ shown above and below, respectively.

Theorems & Definitions (51)

• Theorem 1.1
• Remark 1.2
• Theorem 1.3
• Remark 1.4
• Definition 2.1
• Definition 2.2
• Definition 2.3
• Definition 2.4
• Definition 2.5
• Definition 2.6