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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.

Cite as

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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