Optimal Computation of Avoided Words

  • Yannis Almirantis
  • Panagiotis Charalampopoulos
  • Jia Gao
  • Costas S. Iliopoulos
  • Manal Mohamed
  • Solon P. Pissis
  • Dimitris Polychronopoulos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9838)

Abstract

The deviation of the observed frequency of a word w from its expected frequency in a given sequence x is used to determine whether or not the word is avoided. This concept is particularly useful in DNA linguistic analysis. The value of the standard deviation of w, denoted by \(\textit{std}(w)\), effectively characterises the extent of a word by its edge contrast in the context in which it occurs. A word w of length \(k>2\) is a \(\rho \)-avoided word in x if \(\textit{std}(w) \le \rho \), for a given threshold \(\rho < 0\). Notice that such a word may be completely absent from x. Hence computing all such words naïvely can be a very time-consuming procedure, in particular for large k. In this article, we propose an \(\mathcal {O}(n)\)-time and \(\mathcal {O}(n)\)-space algorithm to compute all \(\rho \)-avoided words of length k in a given sequence x of length n over a fixed-sized alphabet. We also present a time-optimal \(\mathcal {O}(\sigma n)\)-time algorithm to compute all \(\rho \)-avoided words (of any length) in a sequence of length n over an integer alphabet of size \(\sigma \). We provide a tight asymptotic upper bound for the number of \(\rho \)-avoided words over an integer alphabet and the expected length of the longest one. We make available an implementation of our algorithm. Experimental results, using both real and synthetic data, show the efficiency of our implementation.

References

  1. 1.
    Acquisti, C., Poste, G., Curtiss, D., Kumar, S.: Nullomers: really a matter of natural selection? PLoS ONE 2(10), e1022 (2007)CrossRefGoogle Scholar
  2. 2.
    Akalin, A., Fredman, D., Arner, E., Dong, X., Bryne, J., Suzuki, H., Daub, C., Hayashizaki, Y., Lenhard, B.: Transcriptional features of genomic regulatory blocks. Genome Biol. 10(4), 1 (2009)CrossRefGoogle Scholar
  3. 3.
    Barton, C., Heliou, A., Mouchard, L., Pissis, S.P.: Linear-time computation of minimal absent words using suffix array. BMC Bioinform. 15(1), 1–10 (2014)CrossRefGoogle Scholar
  4. 4.
    Barton, C., Heliou, A., Mouchard, L., Pissis, S.P.: Parallelising the computation of minimal absent words. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K., Kitowski, J., Wiatr, K. (eds.) PPAM 2015, Part II. LNCS, vol. 9574, pp. 243–253. Springer, Heidelberg (2016)CrossRefGoogle Scholar
  5. 5.
    Belazzougui, D., Cunial, F.: Space-efficient detection of unusual words. In: Iliopoulos, C., Puglisi, S., Yilmaz, E. (eds.) SPIRE 2015. LNCS, vol. 9309, pp. 222–233. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  6. 6.
    Brendel, V., Beckmann, J.S., Trifonov, E.N.: Linguistics of nucleotide sequences: morphology and comparison of vocabularies. J. Biomol. Struct. Dyn. 4(1), 11–21 (1986)CrossRefGoogle Scholar
  7. 7.
    Crochemore, M., Hancart, C., Lecroq, T.: Algorithms on Strings. Cambridge University Press, New York (2007)CrossRefMATHGoogle Scholar
  8. 8.
    Farach, M.: Optimal suffix tree construction with large alphabets. In: FOCS, pp. 137–143. IEEE (1997)Google Scholar
  9. 9.
    Gawrychowski, P., Lewenstein, M., Nicholson, P.K.: Weighted ancestors in suffix trees. In: Schulz, A.S., Wagner, D. (eds.) ESA 2014. LNCS, vol. 8737, pp. 455–466. Springer, Heidelberg (2014)Google Scholar
  10. 10.
    Mantegna, R.N., Buldyrev, S.V., Goldberger, A.L., Havlin, S., Peng, C.K., Simons, M., Stanley, H.E.: Linguistic features of noncoding DNA sequences. Phys. Rev. Lett. 73, 3169–3172 (1994)CrossRefMATHGoogle Scholar
  11. 11.
    Mignosi, F., Restivo, A., Sciortino, M.: Words and forbidden factors. Theoret. Comput. Sci. 273(1–2), 99–117 (2002)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Rusinov, I., Ershova, A., Karyagina, A., Spirin, S., Alexeevski, A.: Lifespan of restriction-modification systems critically affects avoidance of their recognition sites in host genomes. BMC Genom. 16(1), 1–15 (2015)CrossRefGoogle Scholar
  13. 13.
    Searls, D.B.: The linguistics of DNA. Am. Sci. 80(6), 579–591 (1992)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Yannis Almirantis
    • 1
  • Panagiotis Charalampopoulos
    • 2
  • Jia Gao
    • 2
  • Costas S. Iliopoulos
    • 2
  • Manal Mohamed
    • 2
  • Solon P. Pissis
    • 2
  • Dimitris Polychronopoulos
    • 3
  1. 1.National Center for Scientific Research DemokritosAthensGreece
  2. 2.Department of InformaticsKing’s College LondonLondonUK
  3. 3.Computational Regulatory Genomics, MRC Clinical Sciences CentreImperial College LondonLondonUK

Personalised recommendations