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DOI: 10.4230/LIPIcs.SWAT.2024.3
Pairwise Rearrangement is Fixed-Parameter Tractable in the Single Cut-and-Join Model

Authors: Lora Bailey, Heather Smith Blake, Garner Cochran, Nathan Fox, Michael Levet, Reem Mahmoud, Inne Singgih, Grace Stadnyk, and Alexander Wiedemann

Published in: LIPIcs, Volume 294, 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)

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 #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.
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Lora Bailey, Heather Smith Blake, Garner Cochran, Nathan Fox, Michael Levet, Reem Mahmoud, Inne Singgih, Grace Stadnyk, and Alexander Wiedemann. Pairwise Rearrangement is Fixed-Parameter Tractable in the Single Cut-and-Join Model. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bailey_et_al:LIPIcs.SWAT.2024.3,
  author =	{Bailey, Lora and Blake, Heather Smith and Cochran, Garner and Fox, Nathan and Levet, Michael and Mahmoud, Reem and Singgih, Inne and Stadnyk, Grace and Wiedemann, Alexander},
  title =	{{Pairwise Rearrangement is Fixed-Parameter Tractable in the Single Cut-and-Join Model}},
  booktitle =	{19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)},
  pages =	{3:1--3:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-318-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{294},
  editor =	{Bodlaender, Hans L.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2024.3},
  URN =		{urn:nbn:de:0030-drops-200436},
  doi =		{10.4230/LIPIcs.SWAT.2024.3},
  annote =	{Keywords: Genome Rearrangement, Phylogenetics, Single Cut-and-Join, Computational Complexity}
}
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