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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, Alexander Wiedemann

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Author Details

Lora Bailey
  • Department of Mathematics, Grand Valley State University, Allendale, MI, USA
Heather Smith Blake
  • Department of Mathematics and Computer Science, Davidson College, NC, USA
Garner Cochran
  • Department of Mathematics and Computer Science, Berry College, Mount Berry, GA, USA
Nathan Fox
  • Department of Quantitative Sciences, Canisius University, Buffalo, NY, USA
Michael Levet
  • Department of Computer Science, College of Charleston, SC, USA
Reem Mahmoud
  • Department of Computer Science, Virginia Commonwealth University, Richmond, VA, USA
Inne Singgih
  • Department of Mathematical Sciences, University of Cincinnati, OH, USA
Grace Stadnyk
  • Department of Mathematics, Furman University, Greenville, SC, USA
Alexander Wiedemann
  • Department of Mathematics, Randolph-Macon College, Ashland, VA, USA

Acknowledgements

We wish to thank the American Mathematical Society for organizing the Mathematics Research Community workshop where this work began. This material is based upon work supported by the National Science Foundation under Grant Number DMS 1641020.

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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) https://doi.org/10.4230/LIPIcs.SWAT.2024.3

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity classes
  • Mathematics of computing → Graph theory
Keywords
  • Genome Rearrangement
  • Phylogenetics
  • Single Cut-and-Join
  • Computational Complexity

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References

  1. Lora Bailey, Heather Smith Blake, Garner Cochran, Nathan Fox, Michael Levet, Reem Mahmoud, Elizabeth Bailey Matson, Inne Singgih, Grace Stadnyk, Xinyi Wang, and Alexander Wiedemann. Complexity and enumeration in models of genome rearrangement. In Weili Wu and Guangmo Tong, editors, Computing and Combinatorics, pages 3-14, Cham, 2024. Springer Nature Switzerland. URL: https://doi.org/10.1007/978-3-031-49190-0_1.
  2. Anne Bergeron, Paul Medvedev, and Jens Stoye. Rearrangement models and single-cut operations. Journal of computational biology : a journal of computational molecular cell biology, 17:1213-25, September 2010. URL: https://doi.org/10.1089/cmb.2010.0091.
  3. Marília D. V. Braga and Jens Stoye. Counting all DCJ sorting scenarios. In Francesca D. Ciccarelli and István Miklós, editors, Comparative Genomics, pages 36-47, Berlin, Heidelberg, 2009. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/978-3-642-04744-2_4.
  4. Aaron Darling, István Miklós, and Mark Ragan. Dynamics of genome rearrangement in bacterial populations. PLoS genetics, 4:e1000128, July 2008. URL: https://doi.org/10.1371/journal.pgen.1000128.
  5. Rick Durrett, Rasmus Nielsen, and Thomas York. Bayesian estimation of genomic distance. Genetics, 166:621-9, February 2004. URL: https://doi.org/10.1534/genetics.166.1.621.
  6. Pedro Feijão and Joao Meidanis. SCJ: A breakpoint-like distance that simplifies several rearrangement problems. IEEE/ACM transactions on computational biology and bioinformatics, 8:1318-29, February 2011. URL: https://doi.org/10.1109/TCBB.2011.34.
  7. Andrew Holland and Don Cleveland. Chromoanagenesis and cancer: Mechanisms and consequences of localized, complex chromosomal rearrangements. Nature medicine, 18:1630-8, November 2012. URL: https://doi.org/10.1038/nm.2988.
  8. Mark R. Jerrum, Leslie G. Valiant, and Vijay V. Vazirani. Random generation of combinatorial structures from a uniform distribution. Theoretical Computer Science, 43:169-188, 1986. URL: https://doi.org/10.1016/0304-3975(86)90174-X.
  9. Bret Larget, Donald L. Simon, Joseph B. Kadane, and Deborah Sweet. A Bayesian Analysis of Metazoan Mitochondrial Genome Arrangements. Molecular Biology and Evolution, 22(3):486-495, November 2004. URL: https://doi.org/10.1093/molbev/msi032.
  10. Barbara McClintock. Chromosome organization and genic expression. In Cold Spring Harbor symposia on quantitative biology, volume 16, pages 13-47. Cold Spring Harbor Laboratory Press, 1951. URL: https://doi.org/10.1101/sqb.1951.016.01.004.
  11. István Miklós, Sándor Z. Kiss, and Eric Tannier. Counting and sampling SCJ small parsimony solutions. Theor. Comput. Sci., 552:83-98, 2014. URL: https://doi.org/10.1016/j.tcs.2014.07.027.
  12. István Miklós and Heather Smith. Sampling and counting genome rearrangement scenarios. BMC Bioinformatics, 16:S6, October 2015. URL: https://doi.org/10.1186/1471-2105-16-S14-S6.
  13. István Miklós and Eric Tannier. Bayesian sampling of genomic rearrangement scenarios via double cut and join. Bioinformatics, 26(24):3012-3019, October 2010. URL: https://doi.org/10.1093/bioinformatics/btq574.
  14. István Miklós and Eric Tannier. Approximating the number of double cut-and-join scenarios. Theoretical Computer Science, 439:30-40, 2012. URL: https://doi.org/10.1016/j.tcs.2012.03.006.
  15. J. D. Palmer and L. A. Herbon. Plant mitochondrial dna evolves rapidly in structure, but slowly in sequence. Journal of Molecular Evolution, 28:87-97, December 1988. URL: https://doi.org/10.1007/BF02143500.
  16. A. H. Sturtevant. The linear arrangement of six sex-linked factors in drosophila, as shown by their mode of association. Journal of Experimental Zoology, 14(1):43-59, 1913. URL: https://doi.org/10.1002/jez.1400140104.
  17. A. H. Sturtevant. Genetic factors affecting the strength of linkage in drosophila. Proceedings of the National Academy of Sciences of the United States of America, 3(9):555-558, 1917. URL: http://www.jstor.org/stable/83776.
  18. A. H. Sturtevant. Known and probably inverted sections of the autosomes of Drosophila melanogaster. Carnegie Institution of Washington Publisher, 421:1-27, 1931. Google Scholar
  19. A H Sturtevant and E Novitski. The Homologies of the Chromosome Elements in the genus Drosophila. Genetics, 26(5):517-541, September 1941. URL: https://doi.org/10.1093/genetics/26.5.517.
  20. Sophia Yancopoulos, Oliver Attie, and Richard Friedberg. Efficient sorting of genomic permutations by translocation, inversion and block interchange. Bioinformatics (Oxford, England), 21:3340-6, September 2005. URL: https://doi.org/10.1093/bioinformatics/bti535.
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