QGramProjector: Q-Gram Projection for Indexing Highly-Similar Strings

  • Sebastian Wandelt
  • Ulf Leser
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8133)

Abstract

Q-gram (or n-gram, k-mer) models are used in many research areas, e.g. in computational linguistics for statistical natural language processing, in computer science for approximate string searching, and in computational biology for sequence analysis and data compression. For a collection of N strings, one usually creates a separate positional q-gram index structure for each string, or at least an index structure which needs roughly N times of storage compared to a single string index structure. For highly-similar strings, redundancies can be identified, which do not need to be stored repeatedly; for instance two human genomes have more than 99 percent similarity.

In this work, we propose QGramProjector, a new way of indexing many highly-similar strings. In order to remove the redundancies caused by similarities, our proposal is to 1) create all q-grams for a fixed reference, 2) referentially compress all strings in the collection with respect to the reference, and then 3) project all q-grams from the reference to the compressed strings.

Experiments show that a complete index can be relatively small compared to the collection of highly-similar strings. For a collection of 1092 human genomes (raw data size is 3 TB), a 16-gram index structure, which can be used for instance as a basis for multi-genome read alignment, only needs 100.5 GB (compression ratio of 31:1). We think that our work is an important step towards analysis of large sets of highly-similar genomes on commodity hardware.

Keywords

positional q-grams k-mer large sequences similarity referential compression 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    1000 Genomes Project Consortium. A map of human genome variation from population-scale sequencing. Nature, 467(7319), 1061–1073 (October 2010)Google Scholar
  2. 2.
    Altschul, S.F., Gish, W., Miller, W., Myers, E.W., Lipman, D.J.: Basic local alignment search tool. Journal of Molecular Biology 215(3), 403–410 (1990)Google Scholar
  3. 3.
    Baeza-Yates, R.A., Perleberg, C.H.: Fast and practical approximate string matching. In: Apostolico, A., Galil, Z., Manber, U., Crochemore, M. (eds.) CPM 1992. LNCS, vol. 644, pp. 185–192. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  4. 4.
    Belazzougui, D., Venturini, R.: Compressed string dictionary look-up with edit distance one. In: Kärkkäinen, J., Stoye, J. (eds.) CPM 2012. LNCS, vol. 7354, pp. 280–292. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  5. 5.
    Deorowicz, S., Grabowski, S.: Robust Relative Compression of Genomes with Random Access. Bioinformatics (September 2011)Google Scholar
  6. 6.
    du Mouza, C., Litwin, W., Rigaux, P., Schwarz, T.: As-index: a structure for string search using n-grams and algebraic signatures. In: Proceedings of the 18th ACM Conference on Information and Knowledge Management, CIKM 2009, pp. 295–304. ACM, New York (2009)CrossRefGoogle Scholar
  7. 7.
    Ferragina, P.: String algorithms and data structures. CoRR, abs/0801.2378 (2008)Google Scholar
  8. 8.
    Ferragina, P., Manzini, G.: Indexing compressed text. J. ACM 52(4), 552–581 (2005)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Goto, K., Bannai, H., Inenaga, S., Takeda, M.: Speeding up q-gram mining on grammar-based compressed texts. In: Kärkkäinen, J., Stoye, J. (eds.) CPM 2012. LNCS, vol. 7354, pp. 220–231. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  10. 10.
    Kreft, S., Navarro, G.: On compressing and indexing repetitive sequences. Theor. Comput. Sci. 483, 115–133 (2013)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Kuruppu, S., Puglisi, S., Zobel, J.: Optimized relative lempel-ziv compression of genomes. In: Australasian Computer Science Conference (2011)Google Scholar
  12. 12.
    McCreight, E.: Efficient algorithms for enumerating intersection intervals and rectangles. Technical report, Xerox Paolo Alte Research Center (1980)Google Scholar
  13. 13.
    Navarro, G.: A guided tour to approximate string matching. ACM Comput. Surv. 33(1), 31–88 (2001)CrossRefGoogle Scholar
  14. 14.
    Navarro, G.: Indexing highly repetitive collections. In: Arumugam, S., Smyth, B. (eds.) IWOCA 2012. LNCS, vol. 7643, pp. 274–279. Springer, Heidelberg (2012)Google Scholar
  15. 15.
    Navarro, G., Raffinot, M.: Flexible pattern matching in strings: practical on-line search algorithms for texts and biological sequences. Cambridge University Press, New York (2002)Google Scholar
  16. 16.
    Ohlebusch, E., Fischer, J., Gog, S.: CST++. In: Chavez, E., Lonardi, S. (eds.) SPIRE 2010. LNCS, vol. 6393, pp. 322–333. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  17. 17.
    Reich, D.E., Schaffner, S.F., Daly, M.J., McVean, G., Mullikin, J.C., Higgins, J.M., Richter, D.J., Lander, E.S., Altshuler, D.: Human genome sequence variation and the influence of gene history, mutation and recombination. Nature Genetics 32(1), 135–142 (2002)CrossRefGoogle Scholar
  18. 18.
    Rytter, W.: Application of lempel–ziv factorization to the approximation of grammar-based compression. Theor. Comput. Sci. 302(1-3), 211–222 (2003)MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Sutinen, E., Tarhio, J.: On using q-gram locations in approximate string matching. In: Spirakis, P.G. (ed.) ESA 1995. LNCS, vol. 979, pp. 327–340. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  20. 20.
    Wandelt, S., Leser, U.: Adaptive efficient compression of genomes. Algorithms for Molecular Biology 7, 30 (2012)CrossRefGoogle Scholar
  21. 21.
    Weigel, D., Mott, R.: The 1001 Genomes Project for Arabidopsis thaliana. Genome Biology 10(5), 107+ (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Sebastian Wandelt
    • 1
  • Ulf Leser
    • 1
  1. 1.Knowledge Management in Bioinformatics, Institute for Computer ScienceHumboldt-Universität zu BerlinGermany

Personalised recommendations