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On the Hardness of Approximating Linearization of Scaffolds Sharing Repeated Contigs

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Comparative Genomics (RECOMB-CG 2018)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 11183))

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Abstract

Solutions to genome scaffolding problems can be represented as paths and cycles in a “solution graph”. However, when working with repetitions, such solution graph may contain branchings and they may not be uniquely convertible into sequences. Having introduced, in a previous work, various ways of extracting the unique parts of such solutions, we extend previously known NP-hardness results to the case that the solution graph is planar, bipartite, and subcubic, and show the APX-completeness in this case. We also provide some practical tests.

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References

  1. Berman, P., Karpinski, M., Scott, A.D.: Approximation hardness and satisfiability of bounded occurrence instances of SAT. Electronic Colloquium on Computational Complexity (ECCC), 10(022) (2003)

    Google Scholar 

  2. Biscotti, M.A., Olmo, E., Heslop-Harrison, J.S.: Repetitive DNA in eukaryotic genomes. Chromosome Res. 23(3), 415–420 (2015)

    Article  Google Scholar 

  3. Cameron, D.L., et al.: GRIDSS: sensitive and specific genomic rearrangement detection using positional de Bruijn graph assembly. Genome Res. 27(12), 2050–2060 (2017)

    Article  Google Scholar 

  4. Chateau, A., Giroudeau, R.: A complexity and approximation framework for the maximization scaffolding problem. Theor. Comput. Sci. 595, 92–106 (2015). https://doi.org/10.1016/j.tcs.2015.06.023

    Article  MathSciNet  MATH  Google Scholar 

  5. Chikhi, R., Rizk, G.: Space-efficient and exact de Bruijn graph representation based on a bloom filter. In: Raphael, B., Tang, J. (eds.) WABI 2012. LNCS, vol. 7534, pp. 236–248. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33122-0_19

    Chapter  Google Scholar 

  6. Ekblom, R., Wolf, J.B.: A field guide to whole-genome sequencing, assembly and annotation. Evol. Appl. 7(9), 1026–1042 (2014)

    Article  Google Scholar 

  7. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1979)

    MATH  Google Scholar 

  8. Håstad, J.: Some optimal inapproximability results. J. ACM 48(4), 798–859 (2001)

    Article  MathSciNet  Google Scholar 

  9. Koch, P., Platzer, M., Downie, B.R.: RepARK-de novo creation of repeat libraries from whole-genome NGS reads. Nucleic Acids Res. 42(9), e80 (2014)

    Article  Google Scholar 

  10. Li, H., Durbin, R.: Fast and accurate long-read alignment with Burrows-Wheeler transform. Bioinformatics 26(5), 589–595 (2010)

    Article  Google Scholar 

  11. Li, H., et al.: The sequence alignment/map format and samtools. Bioinformatics 25(16), 2078–2079 (2009)

    Article  Google Scholar 

  12. Lichtenstein, D.: Planar formulae and their uses. SIAM J. Comput. 11(2), 329–343 (1982)

    Article  MathSciNet  Google Scholar 

  13. Lokshtanov, D., Marx, D., Saurabh, S.: Lower bounds based on the exponential time hypothesis. Bull. EATCS 105, 41–72 (2011)

    MathSciNet  MATH  Google Scholar 

  14. Mandric, I., Lindsay, J., Măndoiu, I.I., Zelikovsky, A.: Scaffolding algorithms. In: Măndoiu, I., Zelikovsky, A. (eds.) Computational Methods for Next Generation Sequencing Data Analysis, pp. 107–132. Wiley (2016). Chapter 5

    Google Scholar 

  15. Morgulis, A., Coulouris, G., Raytselis, Y., Madden, T.L., Agarwala, R., Schäffer, A.A.: Database indexing for production megablast searches. Bioinformatics 24(16), 1757–1764 (2008). https://doi.org/10.1093/bioinformatics/btn322

    Article  Google Scholar 

  16. Papadimitriou, C.H., Yannakakis, M.: Optimization, approximation, and complexity classes. J. Comput. Syst. Sci. 43(3), 425–440 (1991)

    Article  MathSciNet  Google Scholar 

  17. Quail, M.A.: A tale of three next generation sequencing platforms: comparison of ion torrent, pacific biosciences and illumina miseq sequencers. BMC Genomics 13(1), 341 (2012)

    Article  Google Scholar 

  18. Tang, H.: Genome assembly, rearrangement, and repeats. Chem. Rev. 107(8), 3391–3406 (2007)

    Article  Google Scholar 

  19. Trevisan, L.: Non-approximability results for optimization problems on bounded degree instances. In: Proceedings on 33rd Annual ACM Symposium on Theory of Computing, 6–8 July 2001, Heraklion, Crete, Greece, pp. 453–461 (2001)

    Google Scholar 

  20. Weller, M., Chateau, A., Giroudeau, R.: Exact approaches for scaffolding. BMC Bioinf. 16(Suppl 14), S2 (2015)

    Article  Google Scholar 

  21. Weller, M., Chateau, A., Giroudeau, R.: On the linearization of scaffolds sharing repeated contigs. In: Gao, X., Du, H., Han, M. (eds.) COCOA 2017. LNCS, vol. 10628, pp. 509–517. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-71147-8_38

    Chapter  Google Scholar 

  22. Weller, M., Chateau, A., Dallard, C., Giroudeau, R.: Scaffolding problems revisited: complexity, approximation and fixed parameter tractable algorithms, and some special cases. Algorithmica 80(6), 1771–1803 (2018)

    Article  MathSciNet  Google Scholar 

  23. Weller, M., Chateau, A., Giroudeau, R., Poss, M.: Scaffolding with repeated contigs using flow formulations (2018)

    Google Scholar 

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Acknowledgments

This work was supported by the Institut de Biologie Computationnelle (http://www.ibc-montpellier.fr/) (ANR Projet Investissements d’Avenir en bioinformatique IBC).

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Authors and Affiliations

  1. LIRMM - CNRS UMR 5506, Montpellier, France

    Tom Davot, Annie Chateau & Rodolphe Giroudeau

  2. IBC, Montpellier, France

    Annie Chateau

  3. CNRS, LIGM, Université Paris Est, Marne-la-Vallée, France

    Mathias Weller

Authors
  1. Tom Davot
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  2. Annie Chateau
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  3. Rodolphe Giroudeau
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  4. Mathias Weller
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Corresponding author

Correspondence to Tom Davot .

Editor information

Editors and Affiliations

  1. McGill University, Montréal, QC, Canada

    Mathieu Blanchette

  2. Université de Sherbrooke, Sherbrooke, QC, Canada

    Aïda Ouangraoua

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Davot, T., Chateau, A., Giroudeau, R., Weller, M. (2018). On the Hardness of Approximating Linearization of Scaffolds Sharing Repeated Contigs. In: Blanchette, M., Ouangraoua, A. (eds) Comparative Genomics. RECOMB-CG 2018. Lecture Notes in Computer Science(), vol 11183. Springer, Cham. https://doi.org/10.1007/978-3-030-00834-5_5

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  • DOI: https://doi.org/10.1007/978-3-030-00834-5_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00833-8

  • Online ISBN: 978-3-030-00834-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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