Pairwise Rearrangement is Fixed-Parameter Tractable in the Single Cut-and-Join Model
Abstract
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 -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 or paths of length . 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.
Cite
@article{arxiv.2402.01942,
title = {Pairwise Rearrangement is Fixed-Parameter Tractable in the Single Cut-and-Join Model},
author = {Lora Bailey and Heather Smith Blake and Garner Cochran and Nathan Fox and Michael Levet and Reem Mahmoud and Inne Singgih and Grace Stadnyk and Alexander Wiedemann},
journal= {arXiv preprint arXiv:2402.01942},
year = {2025}
}
Comments
Full version of paper that appeared in SWAT 2024; arXiv admin note: text overlap with arXiv:2305.01851