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Indexed Matching Statistics and Shortest Unique Substrings

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String Processing and Information Retrieval (SPIRE 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8799))

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Abstract

The unidirectional and bidirectional matching statistics between two strings s and t on alphabet Σ, and the shortest unique substrings of a single string t, are the cornerstone of a number of large-scale genome analysis applications, and they encode nontrivial structural properties of s and t. In this paper we compute for the first time the matching statistics between s and t in O((|s| + |t|)log|Σ|) time and in O(|s|log|Σ|) bits of space, circumventing the need for computing the depths of suffix tree nodes that characterized previous approaches. Symmetrically, we compute for the first time the shortest unique substrings of a string t in O(|t|log|Σ|) time and in O(|t|log|Σ|) bits of space. A key component of our methods is an encoding of both the unidirectional and the bidirectional statistics that takes 2|t| + o(|t|) bits of space and that allows constant-time access to every position.

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References

  1. Belazzougui, D.: Linear time construction of compressed text indices in compact space. In: Proceedings of the 46th ACM Symposium on Theory of Computing. ACM (2014)

    Google Scholar 

  2. Belazzougui, D.: Linear time construction of compressed text indices in compact space. ArXiv preprint ArXiv:1401.0936 (2014)

    Google Scholar 

  3. Belazzougui, D., Navarro, G.: Alphabet-independent compressed text indexing. ACM Transactions on Algorithms (2013) (to appear)

    Google Scholar 

  4. Clark, D.: Compact Pat Trees. PhD thesis, University of Waterloo, Canada (1996)

    Google Scholar 

  5. Farach, M., Noordewier, M., Savari, S., Shepp, L., Wyner, A., Ziv, J.: On the entropy of DNA: Algorithms and measurements based on memory and rapid convergence. In: Proceedings of the Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 48–57 (1995)

    Google Scholar 

  6. Fischer, J., Heun, V.: Space-efficient preprocessing schemes for range minimum queries on static arrays. SIAM Journal on Computing 40(2), 465–492 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Golynski, A.: Optimal lower bounds for rank and select indexes. Theoretical Computer Science 387(3), 348–359 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Haubold, B., Pierstorff, N., Möller, F., Wiehe, T.: Genome comparison without alignment using shortest unique substrings. BMC Bioinformatics 6(1), 123 (2005)

    Article  Google Scholar 

  9. Hon, W.-K., Sadakane, K., Sung, W.-K.: Breaking a time-and-space barrier in constructing full-text indices. SIAM J. Comput. 38(6), 2162–2178 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. İleri, A.M., Külekci, M.O., Xu, B.: Shortest unique substring query revisited. In: Kulikov, A.S., Kuznetsov, S.O., Pevzner, P. (eds.) CPM 2014. LNCS, vol. 8486, pp. 172–181. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  11. Kurtz, S., Phillippy, A., Delcher, A.L., Smoot, M., Shumway, M., Antonescu, C., Salzberg, S.L.: Versatile and open software for comparing large genomes. Genome Biology 5(2), R12 (2004)

    Google Scholar 

  12. Munro, J.I.: Tables. In: Chandru, V., Vinay, V. (eds.) FSTTCS 1996. LNCS, vol. 1180, pp. 37–42. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  13. Ohlebusch, E., Gog, S., Kügel, A.: Computing matching statistics and maximal exact matches on compressed full-text indexes. In: Chavez, E., Lonardi, S. (eds.) SPIRE 2010. LNCS, vol. 6393, pp. 347–358. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  14. Pei, J., Wu, W.-H., Yeh, M.-Y.: On shortest unique substring queries. In: 2013 IEEE 29th International Conference on Data Engineering (ICDE), pp. 937–948. IEEE (2013)

    Google Scholar 

  15. Philippe, N., Salson, M., Commes, T., Rivals, E.: CRAC: An integrated approach to the analysis of RNA-seq reads. Genome Biology 14(3), R30 (2013)

    Google Scholar 

  16. Raman, R., Raman, V., Satti, S.R.: Succinct indexable dictionaries with applications to encoding k-ary trees, prefix sums and multisets. ACM Transactions on Algorithms (TALG) 3(4), 43 (2007)

    Article  MathSciNet  Google Scholar 

  17. Robertson, M.M.: A generalization of quasi-monotone sequences. Proceedings of the Edinburgh Mathematical Society (Series 2) 16(01), 37–41 (1968)

    Article  MATH  Google Scholar 

  18. Sadakane, K.: Compressed suffix trees with full functionality. Theory of Computing Systems 41(4), 589–607 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  19. Schnattinger, T., Ohlebusch, E., Gog, S.: Bidirectional search in a string with wavelet trees and bidirectional matching statistics. Inf. Comput. 213, 13–22 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  20. Tsuruta, K., Inenaga, S., Bannai, H., Takeda, M.: Shortest unique substrings queries in optimal time. In: Geffert, V., Preneel, B., Rovan, B., Štuller, J., Tjoa, A.M. (eds.) SOFSEM 2014. LNCS, vol. 8327, pp. 503–513. Springer, Heidelberg (2014)

    Google Scholar 

  21. Ulitsky, I., Burstein, D., Tuller, T., Chor, B.: The average common substring approach to phylogenomic reconstruction. Journal of Computational Biology 13(2), 336–350 (2006)

    Article  MathSciNet  Google Scholar 

  22. Weiner, P.: The file transmission problem. In: Proceedings of the National Computer Conference and Exposition, June 4-8, pp. 453–453. ACM (1973)

    Google Scholar 

  23. Weiner, P.: Linear pattern matching algorithms. In: Switching and Automata Theory, pp. 1–11. IEEE (1973)

    Google Scholar 

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Belazzougui, D., Cunial, F. (2014). Indexed Matching Statistics and Shortest Unique Substrings. In: Moura, E., Crochemore, M. (eds) String Processing and Information Retrieval. SPIRE 2014. Lecture Notes in Computer Science, vol 8799. Springer, Cham. https://doi.org/10.1007/978-3-319-11918-2_18

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  • DOI: https://doi.org/10.1007/978-3-319-11918-2_18

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11917-5

  • Online ISBN: 978-3-319-11918-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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