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Permuted Pattern Matching on Multi-track Strings

  • Takashi Katsura
  • Kazuyuki Narisawa
  • Ayumi Shinohara
  • Hideo Bannai
  • Shunsuke Inenaga
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7741)

Abstract

We propose a new variant of pattern matching on a multi-set of strings, or multi-tracks, called permuted-matching, that looks for occurrences of a multi-track pattern of length m with M tracks, in a multi-track text of length n with N tracks over Σ. We show that the problem can be solved in O(nNlog|Σ|) time and O(mM + N) space, and further in O(nN) time and space when assuming an integer alphabet. For the case where the number of strings in the text and pattern are equal (full-permuted-matching), we propose a new index structure called the multi-track suffix tree, as well as an O(nN log|Σ|) time and O(nN) space construction algorithm. Using this structure, we can solve the full-permuted-matching problem in O(mN log|Σ| + occ) time for any multi-track pattern of length m with N tracks which occurs occ times.

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References

  1. 1.
    Aho, A., Corasick, M.: Efficient string matching: an aid to bibliographic search. Communications of the ACM 18(6), 333–340 (1975)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Amir, A., Farach, M.: Efficient 2-dimensional approximate matching of non-rectangular figures. In: Proc. SODA 1991, pp. 212–223 (1991)Google Scholar
  3. 3.
    Baker, B.S.: Parameterized pattern matching: Algorithms and applications. J. Comput. Syst. Sci. 52(1), 28–42 (1996)zbMATHCrossRefGoogle Scholar
  4. 4.
    Baker, T.P.: A technique for extending rapid exact-match string matching to arrays of more than one dimension. SIAM Journal on Computing 7(4), 533–541 (1978)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Bird, R.S.: Two dimensional pattern matching. Information Processing Letters 6(5), 168–170 (1977)CrossRefGoogle Scholar
  6. 6.
    Crochemore, M., Rytter, W.: Jewels of Stringology. World Scientific (2002)Google Scholar
  7. 7.
    Dori, S., Landau, G.M.: Construction of Aho Corasick automaton in linear time for integer alphabets. Information Processing Letters 98(2), 66–72 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Farach, M.: Optimal suffix tree construction with large alphabets. In: Proc. FOCS 1997, pp. 137–143 (1997)Google Scholar
  9. 9.
    Gandhi, S., Nath, S., Suri, S., Liu, J.: Gamps: Compressing multi sensor data by grouping and amplitude scaling. In: ACM SIGMOD (2009)Google Scholar
  10. 10.
    Gusfield, D.: Algorithms on Strings, Trees, and Sequences. Cambridge University Press (1997)Google Scholar
  11. 11.
    Ilie, L., Navarro, G., Tinta, L.: The longest common extension problem revisited and applications to approximate string searching. Journal of Discrete Algorithms 8(4), 418–428 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Kärkkäinen, J., Sanders, P., Burkhardt, S.: Linear work suffix array construction. J. ACM 53(6), 918–936 (2006)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Kuruppu, S., Puglisi, S.J., Zobel, J.: Relative Lempel-Ziv Compression of Genomes for Large-Scale Storage and Retrieval. In: Chavez, E., Lonardi, S. (eds.) SPIRE 2010. LNCS, vol. 6393, pp. 201–206. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  14. 14.
    Lemström, K., Mäkinen, V.: On minimizing pattern splitting in multi-track string matching. In: Proc. of CPM 2003, pp. 237–253 (2003)Google Scholar
  15. 15.
    Lemström, K., Tarhio, J.: Transposition invariant pattern matching for multi-track strings. Nordic Journal of Computing 10, 185–205 (2003)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Ukkonen, E.: On-line construction of suffix trees. Algorithmica 14(3), 249–260 (1995)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Takashi Katsura
    • 1
  • Kazuyuki Narisawa
    • 1
  • Ayumi Shinohara
    • 1
  • Hideo Bannai
    • 2
  • Shunsuke Inenaga
    • 2
  1. 1.Graduate School of Information ScienceTohoku UniversityJapan
  2. 2.Department of InformaticsKyushu UniversityJapan

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