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Linear Time Inference of Strings from Cover Arrays Using a Binary Alphabet

(Extended Abstract)
  • Tanaeem M. Moosa
  • Sumaiya Nazeen
  • M. Sohel Rahman
  • Rezwana Reaz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7157)

Abstract

Covers being one of the most popular form of regularities in strings, have drawn much attention over time. In this paper, we focus on the problem of linear time inference of strings from cover arrays using the least sized alphabet possible. We present an algorithm that can reconstruct a string x over a two-letter alphabet whenever a valid cover array C is given as an input. This algorithm uses several interesting combinatorial properties of cover arrays and an interesting relation between border array and cover array to achieve this. Our algorithm runs in linear time.

Keywords

Linear Time Algorithm Sima Linear Time Algorithm Alphabet Size Cover Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading (1974)zbMATHGoogle Scholar
  2. 2.
    Apostolico, A., Breslauer, D.: Of Periods, Quasiperiods, Repetitions and Covers. In: Mycielski, J., Rozenberg, G., Salomaa, A. (eds.) Structures in Logic and Computer Science. LNCS, vol. 1261, pp. 236–248. Springer, Heidelberg (1997), http://dx.doi.org/10.1007/3-540-63246-8_14 CrossRefGoogle Scholar
  3. 3.
    Apostolico, A., Ehrenfeucht, A.: Efficient Detection of Quasiperiodicities in Strings. Theoretical Computer Science 119(2), 247–265 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bannai, H., Inenaga, S., Shinohara, A., Takeda, M.: Inferring Strings from Graphs and Arrays. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 208–217. Springer, Heidelberg (2003), http://dx.doi.org/10.1007/978-3-540-45138-9_15 CrossRefGoogle Scholar
  5. 5.
    Boyer, R.S., Moore, J.S.: A Fast String Searching Algorithm. Communications of the ACM 20(10), 762–772 (1977)CrossRefzbMATHGoogle Scholar
  6. 6.
    Breslauer, D.: An On-Line String Superprimitivity Test. Information Processing Letters 44(6), 345–347 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Clement, J., Crochemore, M., Rindone, G.: Reverse Engineering Prefix Tables. In: Albers, S., Marion, J.Y. (eds.) 26th International Symposium on Theoretical Aspects of Computer Science (STACS 2009). Leibniz International Proceedings in Informatics (LIPIcs), vol. 3, pp. 289–300. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany (2009), http://drops.dagstuhl.de/opus/volltexte/2009/1825 Google Scholar
  8. 8.
    Crochemore, M., Iliopoulos, C.S., Pissis, S.P., Tischler, G.: Cover Array String Reconstruction. In: Amir, A., Parida, L. (eds.) CPM 2010. LNCS, vol. 6129, pp. 251–259. Springer, Heidelberg (2010), http://dx.doi.org/10.1007/978-3-642-13509-5 CrossRefGoogle Scholar
  9. 9.
    Duval, J.P., Lecroq, T., Lefebvre, A.: Border Array on Bounded Alphabet. Journal of Automata, Languages and Combinatorics 10(1), 51–60 (2005)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Franěk, F., Gao, S., Lu, W., Ryan, P.J., Smyth, W.F., Sun, Y., Yang, L.: Verifying a border array in linear time. Journal of Combinatorial Mathematics and Combinatorial Computing 42, 223–236 (2002)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Tomohiro, I., Inenaga, S., Bannai, H., Takeda, M.: Counting Parameterized Border Arrays for a Binary Alphabet. In: Dediu, A.H., Ionescu, A.M., Martín-Vide, C. (eds.) LATA 2009. LNCS, vol. 5457, pp. 422–433. Springer, Heidelberg (2009), http://dx.doi.org/10.1007/978-3-642-00982-2 CrossRefGoogle Scholar
  12. 12.
    Tomohiro, I., Inenaga, S., Bannai, H., Takeda, M.: Verifying a Parameterized Border Array in O(n 1.5) Time. In: Amir, A., Parida, L. (eds.) CPM 2010. LNCS, vol. 6129, pp. 238–250. Springer, Heidelberg (2010), http://dx.doi.org/10.1007/978-3-642-13509-5 CrossRefGoogle Scholar
  13. 13.
    An Implementation of Algorithm MinArrayToString, Website of German Tischler, King’s College London, http://www.kcl.ac.uk/staff/tischler/src/recovering-0.0.0.tar.bz2 (last accessed on December 12, 2010)
  14. 14.
    Knuth, D.E., Morris Jr., J.H., Pratt, V.R.: Fast Pattern Matching in Strings. SIAM Journal on Computing 6(2), 323–350 (1977)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Li, Y., Smyth, W.F.: Computing the Cover Array in Linear Time. Algorithmica 32(1), 95–106 (2002), http://springerlink.metapress.com/openurl.asp?genre=article&issn=0178-4617&volume=32&issue=1&spage=95 MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Nazeen, S., Rahman, M.S., Reaz, R.: Indeterminate String Inference Algorithms. Journal of Discrete Algorithms (in press), http://dx.doi.org/10.1016/j.jda.2011.08.002
  17. 17.
    Smyth, W.F., Wang, S.: New Perspectives on the Prefix Array. In: Amir, A., Turpin, A., Moffat, A. (eds.) SPIRE 2008. LNCS, vol. 5280, pp. 133–143. Springer, Heidelberg (2008), http://dx.doi.org/10.1007/978-3-540-89097-3_14 CrossRefGoogle Scholar
  18. 18.
    A Systematic Annotation Package for Community Analysis of Genomes, University of Wisconsin - Madison, https://asap.ahabs.wisc.edu/asap/download_Source.php?LocationID=&SequenceVersionID=&GenomeID= (last accessed on December 18, 2010)

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Tanaeem M. Moosa
    • 1
  • Sumaiya Nazeen
    • 1
  • M. Sohel Rahman
    • 1
  • Rezwana Reaz
    • 1
  1. 1.AℓEDA Group, Department of CSEBUETDhakaBangladesh

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