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XBWT Tricks

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String Processing and Information Retrieval (SPIRE 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9954))

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Abstract

The eXtended Burrows-Wheeler Transform (XBWT) is a data transformation introduced in [Ferragina et al., FOCS 2005] to compactly represent a labeled tree and simultaneously support navigation and path-search operations over its label structure.

A natural application of the XBWT is to store a dictionary of strings. A recent extensive experimental study [Martínez-Prieto et al., Information Systems, 2016] shows that, among the available string dictionary implementations, the XBWT is attractive because of its good tradeoff between small space usage, speed, and support for substring searches. In this paper we further investigate the use of the XBWT for storing a string dictionary. Our first contribution is to show how to add suffix links (aka failure links) to a XBWT string dictionary. For a XBWT dictionary with n internal nodes our suffix links can be traversed in constant time and only take \(2n + o(n)\) bits of space.

Our second contribution are practical construction algorithms for the XBWT, including the additional data structure supporting the traversal of suffix links. Our algorithms build on the many well engineered algorithms for Suffix Array and BWT construction and offer different tradeoffs between running time and working space.

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Notes

  1. 1.

    The \(\mathsf {RCP}\) array coincides with the \(\mathsf {LCP}\) array if we build the concatenation \(t\) inserting a different symbol $\(_i\) at the end of each string \(x_i\). However, this approach is not practical since would increase significantly the size of the alphabet.

References

  1. Bauer, M.J., Cox, A.J., Rosone, G.: Lightweight algorithms for constructing and inverting the BWT of string collections. Theor. Comput. Sci. 483, 134–148 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  2. Beller, T., Gog, S., Ohlebusch, E., Schnattinger, T.: Computing the longest common prefix array based on the Burrows-Wheeler transform. J. Discrete Algorithms 18, 22–31 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. Beller, T., Zwerger, M., Gog, S., Ohlebusch, E.: Space-efficient construction of the Burrows-Wheeler transform. In: Kurland, O., Lewenstein, M., Porat, E. (eds.) SPIRE 2013. LNCS, vol. 8214, pp. 5–16. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  4. Crochemore, M., Grossi, R., Kärkkäinen, J., Landau, G.M.: Computing the Burrows-Wheeler transform in place and in small space. J. Discrete Algorithms 32, 44–52 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ferragina, P., Gagie, T., Manzini, G.: Lightweight data indexing and compression in external memory. Algorithmica 63, 707–730 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ferragina, P., Luccio, F., Manzini, G., Muthukrishnan, S.: Structuring labeled trees for optimal succinctness, and beyond. In: Proceedings of the 46th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 184–193 (2005)

    Google Scholar 

  7. Ferragina, P., Luccio, F., Manzini, G., Muthukrishnan, S.: Compressing and searching XML data via two zips. In: Proceedings of the 15th International World Wide Web Conference (WWW), pp. 751–760 (2006)

    Google Scholar 

  8. Ferragina, P., Luccio, F., Manzini, G., Muthukrishnan, S.: Compressing and indexing labeled trees, with applications. J. ACM, 57 (2009)

    Google Scholar 

  9. Gusfield, D.: Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology. Cambridge University Press, Cambridge (1997)

    Book  MATH  Google Scholar 

  10. Holt, J., McMillan, L.: Constructing Burrows-Wheeler transforms of large string collections via merging. In: BCB, pp. 464–471. ACM (2014)

    Google Scholar 

  11. Kärkkäinen, J., Manzini, G., Puglisi, S.J.: Permuted longest-common-prefix array. In: Kucherov, G., Ukkonen, E. (eds.) CPM 2009 Lille. LNCS, vol. 5577, pp. 181–192. springer, Heidelberg (2009)

    Chapter  Google Scholar 

  12. Kärkkäinen, J., Kempa, D.: Engineering a lightweight external memory suffix array construction algorithm. In: Proceedings of CEUR Workshop, ICABD, vol. 1146, pp. 53–60 (2014). http://CEUR-WS.org

  13. Kärkkäinen, J., Kempa, D., Puglisi, S.J.: Parallel external memory suffix sorting. In: Cicalese, F., Porat, E., Vaccaro, U. (eds.) CPM 2015. LNCS, vol. 9133, pp. 329–342. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  14. Kasai, T., Lee, G.H., Arimura, H., Arikawa, S., Park, K.: Linear-time longest-common-prefix computation in suffix arrays and its applications. In: Amir, A., Landau, G.M. (eds.) CPM 2001. LNCS, vol. 2089, pp. 181–192. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  15. Knuth, D.E.: Sorting and Searching. The Art of Computer Programming, 2nd edn. Addison-Wesley, Reading (1998)

    Google Scholar 

  16. Li, H.: Fast construction of FM-index for long sequence reads. Bioinformatics 30, 3274–3275 (2014)

    Article  Google Scholar 

  17. Manzini, G.: Two space saving tricks for linear time LCP array computation. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 372–383. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  18. Martínez-Prieto, M.A., Brisaboa, N.R., Cánovas, R., Claude, F., Navarro, G.: Practical compressed string dictionaries. Inf. Syst. 56, 73–108 (2016)

    Article  Google Scholar 

  19. Navarro, G., Sadakane, K.: Fully-functional static and dynamic succinct trees. ACM Trans. Algorithms 10 (2014). Article 16

    Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Science Institute, University of Eastern Piedmont, Alessandria, Italy

    Giovanni Manzini

  2. Institute of Informatics and Telematics, CNR, Pisa, Italy

    Giovanni Manzini

Authors
  1. Giovanni Manzini
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Correspondence to Giovanni Manzini .

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Editors and Affiliations

  1. Kyushu University , Fukuoka, Japan

    Shunsuke Inenaga

  2. Mathematical Informatics, University of Tokyo , Tokyo, Japan

    Kunihiko Sadakane

  3. Computer Science, Waseda University , Tokyo, Japan

    Tetsuya Sakai

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Manzini, G. (2016). XBWT Tricks. In: Inenaga, S., Sadakane, K., Sakai, T. (eds) String Processing and Information Retrieval. SPIRE 2016. Lecture Notes in Computer Science(), vol 9954. Springer, Cham. https://doi.org/10.1007/978-3-319-46049-9_8

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  • DOI: https://doi.org/10.1007/978-3-319-46049-9_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46048-2

  • Online ISBN: 978-3-319-46049-9

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