Advertisement

A Faster Implementation of Online Run-Length Burrows-Wheeler Transform

  • Tatsuya Ohno
  • Yoshimasa Takabatake
  • Tomohiro I
  • Hiroshi Sakamoto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10765)

Abstract

Run-length encoding Burrows-Wheeler Transformed strings, resulting in Run-Length BWT (RLBWT), is a powerful tool for processing highly repetitive strings. We propose a new algorithm for online RLBWT working in run-compressed space, which runs in \(O(n\lg r)\) time and \(O(r\lg n)\) bits of space, where n is the length of input string S received so far and r is the number of runs in the BWT of the reversed S. We improve the state-of-the-art algorithm for online RLBWT in terms of empirical construction time. Adopting the dynamic list for maintaining a total order, we can replace rank queries in a dynamic wavelet tree on a run-length compressed string by the direct comparison of labels in a dynamic list. The empirical result for various benchmarks show the efficiency of our algorithm, especially for highly repetitive strings.

Notes

Acknowledgments

This work was supported by JST CREST (Grant Number JPMJCR1402), and KAKENHI (Grant Numbers 17H01791 and 16K16009).

References

  1. 1.
    DYNAMIC: Dynamic succinct/compressed data structures library. https://github.com/xxsds/DYNAMIC
  2. 2.
  3. 3.
    Get-git-revisions: Get all revisions of a git repository. https://github.com/nicolaprezza/get-git-revisions
  4. 4.
    Belazzougui, D., Cunial, F., Gagie, T., Prezza, N., Raffinot, M.: Composite repetition-aware data structures. In: Cicalese, F., Porat, E., Vaccaro, U. (eds.) CPM 2015. LNCS, vol. 9133, pp. 26–39. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-19929-0_3CrossRefGoogle Scholar
  5. 5.
    Bender, M.A., Cole, R., Demaine, E.D., Farach-Colton, M., Zito, J.: Two simplified algorithms for maintaining order in a list. In: Möhring, R., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 152–164. Springer, Heidelberg (2002).  https://doi.org/10.1007/3-540-45749-6_17CrossRefzbMATHGoogle Scholar
  6. 6.
    Bille, P., Cording, P.H., Gørtz, I.L., Skjoldjensen, F.R., Vildhøj, H.W., Vind, S.: Dynamic relative compression, dynamic partial sums, and substring concatenation. In: ISAAC, pp. 18:1–18:13 (2016)Google Scholar
  7. 7.
    Bowe, A., Onodera, T., Sadakane, K., Shibuya, T.: Succinct de Bruijn graphs. In: Raphael, B., Tang, J. (eds.) WABI 2012. LNCS, vol. 7534, pp. 225–235. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-33122-0_18CrossRefGoogle Scholar
  8. 8.
    Burrows, M., Wheeler, D.J.: A block-sorting lossless data compression algorithm. Technical report, HP Labs (1994)Google Scholar
  9. 9.
    Ferragina, P., Luccio, F., Manzini, G., Muthukrishnan, S.: Structuring labeled trees for optimal succinctness, and beyond. In: FOCS, pp. 184–196 (2005)Google Scholar
  10. 10.
    Ferragina, P., Manzini, G.: Opportunistic data structures with applications. In: FOCS, pp. 390–398 (2000)Google Scholar
  11. 11.
    Hon, W., Sadakane, K., Sung, W.: Succinct data structures for searchable partial sums with optimal worst-case performance. Theor. Comput. Sci. 412(39), 5176–5186 (2011)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Mäkinen, V., Navarro, G., Sirén, J., Välimäki, N.: Storage and retrieval of highly repetitive sequence collections. J. Comput. Biol. 17(3), 281–308 (2010)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Munro, J.I., Nekrich, Y.: Compressed data structures for dynamic sequences. In: Bansal, N., Finocchi, I. (eds.) ESA 2015. LNCS, vol. 9294, pp. 891–902. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-48350-3_74CrossRefGoogle Scholar
  14. 14.
    Navarro, G., Nekrich, Y.: Optimal dynamic sequence representations. SIAM J. Comput. 43(5), 1781–1806 (2014)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Navarro, G., Sadakane, K.: Fully functional static and dynamic succinct trees. ACM Trans. Algorithms 10(3), 16 (2014)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Policriti, A., Prezza, N.: Computing LZ77 in run-compressed space. In: DCC, pp. 23–32 (2016)Google Scholar
  17. 17.
    Prezza, N.: A framework of dynamic data structures for string processing. In: SEA (2017 to appear)Google Scholar
  18. 18.
    Sirén, J.: Compressed Full-Text Indexes for Highly Repetitive Collections. Ph.D. thesis, University of Helsinki (2012)Google Scholar
  19. 19.
    Sirén, J., Välimäki, N., Mäkinen, V., Navarro, G.: Run-length compressed indexes are superior for highly repetitive sequence collections. In: Amir, A., Turpin, A., Moffat, A. (eds.) SPIRE 2008. LNCS, vol. 5280, pp. 164–175. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-89097-3_17CrossRefGoogle Scholar
  20. 20.
    Ziv, J., Lempel, A.: A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory IT 23(3), 337–349 (1977)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Tatsuya Ohno
    • 1
  • Yoshimasa Takabatake
    • 1
  • Tomohiro I
    • 1
  • Hiroshi Sakamoto
    • 1
  1. 1.Kyushu Institute of TechnologyIizukaJapan

Personalised recommendations