eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2024-05-31
3:1
3:16
10.4230/LIPIcs.SWAT.2024.3
article
Pairwise Rearrangement is Fixed-Parameter Tractable in the Single Cut-and-Join Model
Bailey, Lora
1
Blake, Heather Smith
2
Cochran, Garner
3
Fox, Nathan
4
Levet, Michael
5
Mahmoud, Reem
6
Singgih, Inne
7
Stadnyk, Grace
8
Wiedemann, Alexander
9
Department of Mathematics, Grand Valley State University, Allendale, MI, USA
Department of Mathematics and Computer Science, Davidson College, NC, USA
Department of Mathematics and Computer Science, Berry College, Mount Berry, GA, USA
Department of Quantitative Sciences, Canisius University, Buffalo, NY, USA
Department of Computer Science, College of Charleston, SC, USA
Department of Computer Science, Virginia Commonwealth University, Richmond, VA, USA
Department of Mathematical Sciences, University of Cincinnati, OH, USA
Department of Mathematics, Furman University, Greenville, SC, USA
Department of Mathematics, Randolph-Macon College, Ashland, VA, USA
Genome rearrangement is a common model for molecular evolution. In this paper, we consider the Pairwise Rearrangement problem, which takes as input two genomes and asks for the number of minimum-length sequences of permissible operations transforming the first genome into the second. In the Single Cut-and-Join model (Bergeron, Medvedev, & Stoye, J. Comput. Biol. 2010), Pairwise Rearrangement is #P-complete (Bailey, et. al., COCOON 2023), which implies that exact sampling is intractable. In order to cope with this intractability, we investigate the parameterized complexity of this problem. We exhibit a fixed-parameter tractable algorithm with respect to the number of components in the adjacency graph that are not cycles of length 2 or paths of length 1. As a consequence, we obtain that Pairwise Rearrangement in the Single Cut-and-Join model is fixed-parameter tractable by distance. Our results suggest that the number of nontrivial components in the adjacency graph serves as the key obstacle for efficient sampling.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol294-swat2024/LIPIcs.SWAT.2024.3/LIPIcs.SWAT.2024.3.pdf
Genome Rearrangement
Phylogenetics
Single Cut-and-Join
Computational Complexity