New Results About the Linearization of Scaffolds Sharing Repeated Contigs

  • Dorine Tabary
  • Tom DavotEmail author
  • Mathias Weller
  • Annie Chateau
  • Rodolphe Giroudeau
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11346)


Solutions to genome scaffolding problems can be represented as paths and cycles in a “solution graph”. However, when working with repetitions, such solution graphs may contain branchings and, thus, they may not be uniquely convertible into sequences. Having introduced 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 that there is no PTAS in this case.



This work was supported by the Institut de Biologie Computationnelle3 ( (ANR Projet Investissements d’Avenir en bioinformatique IBC) and the “Région Occitanie”.


  1. 1.
    Berg, M.D., Khosravi, A.: Optimal binary space partitions for segments in the plane. Int. J. Comput. Geom. Appl. 22(3), 187–206 (2012)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Berman, P., Karpinski, M., Scott, A.D.: Approximation hardness and satisfiability of bounded occurrence instances of SAT. Electronic Colloquium on Computational Complexity (ECCC), vol. 10, no. 022 (2003)Google Scholar
  3. 3.
    Biscotti, M.A., Olmo, E., Heslop-Harrison, J.S.: Repetitive DNA in eukaryotic genomes. Chromosome Res. 23(3), 415–420 (2015)CrossRefGoogle Scholar
  4. 4.
    Chateau, A., Giroudeau, R.: A complexity and approximation framework for the maximization scaffolding problem. Theor. Comput. Sci. 595, 92–106 (2015). Scholar
  5. 5.
    Davot, T., Chateau, A., Giroudeau, R., Weller, M.: On the hardness of approximating the linearization of scaffolds sharing repeated contigs, Accepted to RecombCG 2018Google Scholar
  6. 6.
    Håstad, J.: Some optimal inapproximability results. J. ACM 48(4), 798–859 (2001)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Hunt, M., Newbold, C., Berriman, M., Otto, T.: A comprehensive evaluation of assembly scaffolding tools. Genome Biol. 15(3), R42 (2014)CrossRefGoogle Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    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, Chap. 5, pp. 107–132. Wiley (2016)Google Scholar
  10. 10.
    Papadimitriou, C.H., Yannakakis, M.: Optimization, approximation, and complexity classes. J. Comput. Syst. Sci. 43(3), 425–440 (1991)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Philippe, N., Salson, M., Lecroq, T., Léonard, M., Commes, T., Rivals, E.: Querying large read collections in main memory: a versatile data structure. BMC Bioinform. 12, 242 (2011). Scholar
  12. 12.
    Quail, M., et al.: A tale of three next generation sequencing platforms: comparison of ion torrent, pacific biosciences and illumina miseq sequencers. BMC Genomics 13(1), 341 (2012)CrossRefGoogle Scholar
  13. 13.
    Tang, H.: Genome assembly, rearrangement, and repeats. Chem. Rev. 107(8), 3391–3406 (2007)CrossRefGoogle Scholar
  14. 14.
    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)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Weller, M., Chateau, A., Giroudeau, R.: Exact approaches for scaffolding. BMC Bioinform. 16(Suppl. 14), S2 (2015)CrossRefGoogle Scholar
  16. 16.
    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). Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Dorine Tabary
    • 1
  • Tom Davot
    • 1
    Email author
  • Mathias Weller
    • 2
  • Annie Chateau
    • 1
  • Rodolphe Giroudeau
    • 1
  1. 1.LIRMM - CNRS UMR 5506MontpellierFrance
  2. 2.CNRS, LIGMParisFrance

Personalised recommendations