Skip to main content
SpringerLink
Log in

Resequencing a Set of Strings Based on a Target String

  • Published:
Algorithmica Aims and scope Submit manuscript

Abstract

Given a set S={S 1,S 2,…,S l } of l strings, a text T, and a natural number k, find a string M, which is a concatenation of k strings (not necessarily distinct, i.e., a string in S may occur more than once in M) from S, whose longest common subsequence with T is largest, where a string in S may occur more than once in M. Such a string is called a k-inlay. The resequencing longest common subsequence problem (resequencing LCS problem for short) is to find a k-inlay for each query with parameter k after T and S are given. In this paper, we propose an algorithm for solving this problem which takes O(nml) preprocessing time and O(ϑ k k) query time for each query with parameter k, where n is the length of T, m is the maximal length of strings in S, and ϑ k is the length of the longest common subsequence between a k-inlay and T.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Aggarwal, A., Klawe, M.M., Moran, S., Shor, P., Wilber, R.: Geometric applications of a matrix-searching algorithm. Algorithmica 2(1), 195–208 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  2. Aho, A., Hirschberg, D., Ullman, J.: Bounds on the complexity of the longest common subsequence problem. J. ACM 23(1), 1–12 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  3. Alves, C.E.R., Cáceres, E.N., Song, S.W.: An all-substrings common subsequence algorithm. Discrete Appl. Math. 156(7), 1025–1035 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  4. Amir, A., Hartman, T., Kapah, O., Shalom, R., Tsur, D.: Generalized LCS. Theor. Comput. Sci. 409(3), 438–449 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  5. Amir, A., Gothilf, T., Shalom, R.: Weighted LCS. In: Proceedings of Combinatorial Algorithms: 20th International Workshop, IWOCA 2009, pp. 36–47 (2009)

    Chapter  Google Scholar 

  6. Bein, W.W., Golin, M.J., Larmore, L.L., Zhang, Y.: The Knuth-Yao quadrangle-inequality speedup is a consequence of total-monotonicity. In: Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2006), pp. 31–40 (2006)

    Google Scholar 

  7. Bergroth, L., Hakonen, H., Raita, T.: A survey of longest common subsequence algorithms. In: Proceedings of 7th Symposium on String Processing and Information Retrieval (SPIRE 2000), pp. 39–48 (2000)

    Chapter  Google Scholar 

  8. Brent, R.P.: The parallel evaluation of general arithmetic expressions. J. ACM 21, 201–206 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  9. Burkard, R.E.: Monge properties, discrete convexity and applications. Eur. J. Oper. Res. 176(1), 1–14 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  10. Burkard, R.E., Klinz, B., Rudolf, R.: Perspectives of Monge properties in optimization. Discrete Appl. Math. 70(2), 95–161 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  11. Chvatal, V., Klarner, D.A., Knuth, D.E.: Selected combinatorial research problem. Technical Report CS-TR-72-292, Stanford University (1972)

  12. Demaine, E.D., Mozes, S., Rossman, B., Weimann, O.: An optimal decomposition algorithm for tree edit distance. In: Proc. 34th International Colloquium on Automata, Languages and Programming (ICALP). Lecture Notes in Computer Science, vol. 4596, pp. 146–157 (2007)

    Chapter  Google Scholar 

  13. Gusfield, D.: Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology. Cambridge University Press, Cambridge (1997)

    Book  MATH  Google Scholar 

  14. Hirschberg, D.S.: Algorithms for the longest common subsequence problem. J. ACM 24(4), 664–675 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  15. Huang, K.S., Yang, C.B., Tseng, K.T., Peng, Y.H., Ann, H.Y.: Dynamic programming algorithms for the mosaic longest common subsequence problem. Inf. Process. Lett. 102, 99–103 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  16. Knuth, D.E.: The Art of Computer Programming, pp. 560–563. Addison-Wesley, Reading (1973)

    Google Scholar 

  17. Komatsoulis, G.A., Waterman, M.S.: Chimeric alignment by dynamic programming: algorithm and biological uses. In: RECOMB97: Proceedings of the First Annual International Conference on Computational Molecular Biology, pp. 174–180. ACM Press, New York (1997)

    Chapter  Google Scholar 

  18. Komatsoulis, G.A., Waterman, M.S.: A new computational method for detection of chimeric 16S rRNA artifacts generated by PCR amplification from mixed bacterial populations. Appl. Environ. Microbiol. 63(6), 2338–2346 (1997)

    Google Scholar 

  19. Landau, G.M., Ziv-Ukelson, M.: On the common substring alignment problem. J. Algorithms 41(2), 338–359 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  20. Liu, J.J., Wang, Y.L., Lee, R.C.T.: Finding a longest common subsequence between a run-length-encoded string and an uncompressed string. J. Complex. 24, 173–184 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  21. Masek, W.J., Paterson, M.S.: A faster algorithm computing string edit distances. J. Comput. Syst. Sci. 20, 18–31 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  22. Modelevsky, J.: Computer applications in applied genetic engineering. Adv. Appl. Microbiol. 30, 169–195 (1984)

    Article  Google Scholar 

  23. Wagner, R.A., Fischer, M.J.: The string-to-string correction problem. J. ACM 21(1), 168–173 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  24. Zhang, K., Shasha, D.: Simple fast algorithms for the editing distance between trees and related problems. SIAM J. Comput. 18(6), 1245–1262 (1989)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors would like to thank anonymous referees for their careful reading with corrections and useful comments which helped to improve the paper.

Author information

Authors and Affiliations

  1. Department of Information Management, National Taiwan University of Science and Technology, Taipei, Taiwan

    Chih-En Kuo & Yue-Li Wang

  2. Department of Information Management, Shih Hsin University, Taipei, Taiwan

    Jia-Jie Liu

  3. Institute of Information Science, Academia Sinica, Taipei, Taiwan

    Ming-Tat Ko

Authors
  1. Chih-En Kuo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yue-Li Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jia-Jie Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ming-Tat Ko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yue-Li Wang.

Additional information

This work was supported in part by the National Science Council of the Republic of China under contracts NSC 100-2221-E-011-067-MY3 and NSC 101-2221-E-011-038-MY3.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kuo, CE., Wang, YL., Liu, JJ. et al. Resequencing a Set of Strings Based on a Target String. Algorithmica 72, 430–449 (2015). https://doi.org/10.1007/s00453-013-9859-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00453-013-9859-z

Keywords

Search

Navigation