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

(Extended Abstract)

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Part of the Lecture Notes in Computer Science book series (LNTCS,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.

The authors’ names are in the alphabetical order of their last names. This research was part of the undergraduate research work of Nazeen and Reaz under the supervision of Rahman.

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References

  1. Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading (1974)

    MATH  Google Scholar 

  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

    CrossRef  Google Scholar 

  3. Apostolico, A., Ehrenfeucht, A.: Efficient Detection of Quasiperiodicities in Strings. Theoretical Computer Science 119(2), 247–265 (1993)

    CrossRef  MathSciNet  MATH  Google Scholar 

  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

    CrossRef  Google Scholar 

  5. Boyer, R.S., Moore, J.S.: A Fast String Searching Algorithm. Communications of the ACM 20(10), 762–772 (1977)

    CrossRef  MATH  Google Scholar 

  6. Breslauer, D.: An On-Line String Superprimitivity Test. Information Processing Letters 44(6), 345–347 (1992)

    CrossRef  MathSciNet  MATH  Google Scholar 

  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. 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

    CrossRef  Google Scholar 

  9. Duval, J.P., Lecroq, T., Lefebvre, A.: Border Array on Bounded Alphabet. Journal of Automata, Languages and Combinatorics 10(1), 51–60 (2005)

    MathSciNet  MATH  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  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

    CrossRef  Google Scholar 

  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

    CrossRef  Google Scholar 

  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. Knuth, D.E., Morris Jr., J.H., Pratt, V.R.: Fast Pattern Matching in Strings. SIAM Journal on Computing 6(2), 323–350 (1977)

    CrossRef  MathSciNet  MATH  Google Scholar 

  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

    CrossRef  MathSciNet  MATH  Google Scholar 

  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. 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

    CrossRef  Google Scholar 

  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)

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Moosa, T.M., Nazeen, S., Rahman, M.S., Reaz, R. (2012). Linear Time Inference of Strings from Cover Arrays Using a Binary Alphabet. In: Rahman, M.S., Nakano, Si. (eds) WALCOM: Algorithms and Computation. WALCOM 2012. Lecture Notes in Computer Science, vol 7157. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28076-4_17

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  • DOI: https://doi.org/10.1007/978-3-642-28076-4_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28075-7

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