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Documents authored by Mahmoud, Reem

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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}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2023.9
Minimum Separator Reconfiguration

Authors: Guilherme C. M. Gomes, Clément Legrand-Duchesne, Reem Mahmoud, Amer E. Mouawad, Yoshio Okamoto, Vinicius F. dos Santos, and Tom C. van der Zanden

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

Abstract
We study the problem of reconfiguring one minimum s-t-separator A into another minimum s-t-separator B in some n-vertex graph G containing two non-adjacent vertices s and t. We consider several variants of the problem as we focus on both the token sliding and token jumping models. Our first contribution is a polynomial-time algorithm that computes (if one exists) a minimum-length sequence of slides transforming A into B. We additionally establish that the existence of a sequence of jumps (which need not be of minimum length) can be decided in polynomial time (by an algorithm that also outputs a witnessing sequence when one exists). In contrast, and somewhat surprisingly, we show that deciding if a sequence of at most 𝓁 jumps can transform A into B is an NP-complete problem. To complement this negative result, we investigate the parameterized complexity of what we believe to be the two most natural parameterized counterparts of the latter problem; in particular, we study the problem of computing a minimum-length sequence of jumps when parameterized by the size k of the minimum s-t-separators and when parameterized by the number 𝓁 of jumps. For the first parameterization, we show that the problem is fixed-parameter tractable, but does not admit a polynomial kernel unless NP ⊆ coNP/poly. We complete the picture by designing a kernel with 𝒪(𝓁²) vertices and edges for the length 𝓁 of the sequence as a parameter.
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Guilherme C. M. Gomes, Clément Legrand-Duchesne, Reem Mahmoud, Amer E. Mouawad, Yoshio Okamoto, Vinicius F. dos Santos, and Tom C. van der Zanden. Minimum Separator Reconfiguration. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 9:1-9:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{c.m.gomes_et_al:LIPIcs.IPEC.2023.9,
  author =	{C. M. Gomes, Guilherme and Legrand-Duchesne, Cl\'{e}ment and Mahmoud, Reem and Mouawad, Amer E. and Okamoto, Yoshio and F. dos Santos, Vinicius and C. van der Zanden, Tom},
  title =	{{Minimum Separator Reconfiguration}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{9:1--9:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.9},
  URN =		{urn:nbn:de:0030-drops-194288},
  doi =		{10.4230/LIPIcs.IPEC.2023.9},
  annote =	{Keywords: minimum separators, combinatorial reconfiguration, parameterized complexity, kernelization}
}
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