Compact Universal k-mer Hitting Sets

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9838)

Abstract

We address the problem of finding a minimum-size set of k-mers that hits L-long sequences. The problem arises in the design of compact hash functions and other data structures for efficient handling of large sequencing datasets. We prove that the problem of hitting a given set of L-long sequences is NP-hard and give a heuristic solution that finds a compact universal k-mer set that hits any set of L-long sequences. The algorithm, called DOCKS (design of compact k-mer sets), works in two phases: (i) finding a minimum-size k-mer set that hits every infinite sequence; (ii) greedily adding k-mers such that together they hit all remaining L-long sequences. We show that DOCKS works well in practice and produces a set of k-mers that is much smaller than a random choice of k-mers. We present results for various values of k and sequence lengths L and by applying them to two bacterial genomes show that universal hitting k-mers improve on minimizers. The software and exemplary sets are freely available at acgt.cs.tau.ac.il/docks/.

References

  1. 1.
    Grabowski, S., Raniszewski, M.: Sampling the suffix array with minimizers. In: Iliopoulos, C., Puglisi, S., Yilmaz, E. (eds.) SPIRE 2015. LNCS, vol. 9309, pp. 287–298. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  2. 2.
    Roberts, M., Hayes, W., Hunt, B.R., Mount, S.M., Yorke, J.A.: Reducing storage requirements for biological sequence comparison. Bioinformatics 20, 3363–3369 (2004)CrossRefGoogle Scholar
  3. 3.
    Karkkainen, J., Ukkonen, E.: Sparse suffix trees. In: Cai, J.-Y., Wong, C.K. (eds.) COCOON 1996. LNCS, vol. 1090, pp. 219–230. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  4. 4.
    Solomon, B., Kingsford, C.: Fast search of thousands of short-read sequencing experiments. Nat. Biotechnol. 34, 300–302 (2016)CrossRefGoogle Scholar
  5. 5.
    Movahedi, N.S., Forouzmand, E., Chitsaz, H.: De novo co-assembly of bacterial genomes from multiple single cells. In: 2012 IEEE International Conference on Bioinformatics and Biomedicine (BIBM), pp. 1–5 (2012)Google Scholar
  6. 6.
    Deorowicz, S., Kokot, M., Grabowski, S., Debudaj-Grabysz, A.: KMC 2: fast and resource-frugal \(k\)-mer counting. Bioinformatics 31(10), 1569–1576 (2015). Oxford Univ PressCrossRefGoogle Scholar
  7. 7.
    Chikhi, R., Limasset, A., Jackman, S., Simpson, J.T., Medvedev, P.: On the representation of de Bruijn graphs. J. Comput. Biol. 22, 336–352 (2015)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Li, Y., Kamousi, P., Han, F., Yang, S., Yan, X., Suri, S.: Memory efficient minimum substring partitioning. In: Proceedings of the VLDB Endowment, vol. 6, pp. 169–180. VLDB Endowment (2013)Google Scholar
  9. 9.
    Ye, C., Ma, Z.S., Cannon, C.H., Pop, M., Douglas, W.Y.: Exploiting sparseness in de novo genome assembly. BMC Bioinform. 13, S1 (2012)CrossRefGoogle Scholar
  10. 10.
    Wood, D.E., Salzberg, S.L.: Kraken: ultrafast metagenomic sequence classification using exact alignments. Genome Biol. 15, R46 (2014)CrossRefGoogle Scholar
  11. 11.
    Sahinalp, S.C., Vishkin, U.: Efficient approximate and dynamic matching of patterns using a labeling paradigm. In: 37th Annual Symposium on Foundations of Computer Science, Proceedings, pp. 320–328 (1996)Google Scholar
  12. 12.
    Hach, F., Numanagi, I., Alkan, C., Sahinalp, S.C.: SCALCE: boosting sequence compression algorithms using locally consistent encoding. Bioinformatics 28, 3051–3057 (2012)CrossRefGoogle Scholar
  13. 13.
    Mykkeltveit, J.: A proof of Golomb’s conjecture for the de Bruijn graph. J. Comb. Theory Ser. B 13, 40–45 (1972)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
  15. 15.
    Champarnaud, J.M., Hansel, G., Perrin, D.: Unavoidable sets of constant length. Int. J. Algebra Comput. 14, 241–251 (2004)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Chvatal, V.: A greedy heuristic for the set-covering problem. Math. Oper. Res. 4, 233–235 (1979)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Karp, R.M.: Reducibility among combinatorial problems. In: Jünger, M., Liebling, T.M., Naddef, D., Nemhauser, G.L., Pulleyblank, W.R., Reinelt, G., Rinaldi, G., Wolsey, L.A. (eds.) 50 Years of Integer Programming 1958–2008, pp. 219–241. Springer, Heidelberg (2010)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Computer Science and Artificial Intelligence LaboratoryMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Blavatnik School of Computer ScienceTel-Aviv UniversityTel-avivIsrael
  3. 3.School of Computer ScienceCarnegie Mellon UniversityPittsburghUSA

Personalised recommendations