Inferring Strings from Graphs and Arrays

  • Hideo Bannai
  • Shunsuke Inenaga
  • Ayumi Shinohara
  • Masayuki Takeda
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2747)


This paper introduces a new problem of inferring strings from graphs, and inferring strings from arrays. Given a graph G or an array A, we infer a string that suits the graph, or the array, under some condition. Firstly, we solve the problem of finding a string w such that the directed acyclic subsequence graph (DASG) of w is isomorphic to a given graph G. Secondly, we consider directed acyclic word graphs (DAWGs) in terms of string inference. Finally, we consider the problem of finding a string w of a minimal size alphabet, such that the suffix array (SA) of w is identical to a given permutation p=p1,...,pn of integers 1,...,n. Each of our three algorithms solving the above problems runs in linear time with respect to the input size.


  1. 1.
    Crochemore, M., Rytter, W.: Jewels of Stringology. World Scientific, Singapore (2002)CrossRefGoogle Scholar
  2. 2.
    Baeza-Yates, R.A.: Searching subsequences (note). Theoretical Computer Science 78, 363–376 (1991)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Blumer, A., Blumer, J., Haussler, D., Ehrenfeucht, A., Chen, M.T., Seiferas, J.: The smallest automaton recognizing the subwords of a text. Theoretical Computer Science 40, 31–55 (1985)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Franěk, F., Gao, S., Lu, W., Ryan, P.J., Smyth, W.F., Sun, Y., Yang, L.: Verifying a border array in linear time. J. Comb. Math. Comb. Comput., 223–236 (2002)Google Scholar
  5. 5.
    Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The design and analysis of computer algorithms. Addison-Wesley, Reading (1974)MATHGoogle Scholar
  6. 6.
    Duval, J.P., Lecroq, T., Lefevre, A.: Border array on bounded alphabet. In: Proc. The Prague Stringology Conference 2002 (PSC 2002), pp. 28–35. Czech Technical University (2002)Google Scholar
  7. 7.
    Manber, U., Myers, G.: Suffix arrays: A new method for on-line string searches. SIAM J. Compt. 22, 935–948 (1993)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Atallah, M.J. (ed.): Algorithms and Theory of Computation Handbook. CRC Press, Boca Raton (1998) ISBN:0-8493-2649-4MATHGoogle Scholar
  9. 9.
    Crochemore, M.: Transducers and repetitions. Theoretical Computer Science 45, 63–86 (1986)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Graham, R., Knuth, D., Patashnik, O.: Concrete Mathematics, 2nd edn. Addison Wesley, Reading (1994)MATHGoogle Scholar
  11. 11.
    Allauzen, C., Crochemore, M., Raffinot, M.: Factor oracle: A new structure for pattern matching. In: Bartosek, M., Tel, G., Pavelka, J. (eds.) SOFSEM 1999. LNCS, vol. 1725, pp. 291–306. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  12. 12.
    Weiner, P.: Linear pattern matching algorithms. In: Proc. 14th Annual Symposium on Switching and Automata Theory, pp. 1–11 (1973)Google Scholar
  13. 13.
    Blumer, A., Blumer, J., Haussler, D., McConnell, R., Ehrenfeucht, A.: Complete inverted files for efficient text retrieval and analysis. Journal of the ACM 34, 578–595 (1987)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Hideo Bannai
    • 1
  • Shunsuke Inenaga
    • 2
  • Ayumi Shinohara
    • 2
    • 3
  • Masayuki Takeda
    • 2
    • 3
  1. 1.Human Genome Center, Institute of Medical ScienceUniversity of TokyoMinato-ku, TokyoJapan
  2. 2.Department of InformaticsFukuokaJapan
  3. 3.PRESTOJapan Science and Technology Corporation (JST) 

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