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Some Approximations for Shortest Common Nonsubsequences and Supersequences

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String Processing and Information Retrieval (SPIRE 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5280))

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Abstract

This paper is devoted to polynomial-time approximations for the problems of finding a shortest common nonsubsequence and a shortest common supersequence of given strings. The main attention is paid to the special case of the latter problem where all given strings are of length two. We show strong connections of this case to the feedback vertex set problem, the maximal network flow problem and the maximal multi-commodity network flow problem.

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References

  1. Bafna, V., Lawler, E.L., Pevzner, P.A.: Approximation algorithms for multiple sequence alignment. Theoret. Comput. Sci. 182, 233–244 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  2. Barone, P., Bonzzoni, P., Vedova, G.D., Mauri, G.: An approximation algorithm for the shortset common supersequence problem: an experimental analysis. In: Proc. of the 2001 ACM Symp. on Applied Comput., Las Vegas, March 11-14, pp. 56–60 (2001)

    Google Scholar 

  3. Cotta, C.: Memetic algorithms with partial lamarckism for the shortest common supersequence problem. In: Mira, J., Álvarez, J.R. (eds.) IWINAC 2005, vol. 3562, pp. 84–91. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  4. Cotta, C.: A comparison of evolutionary approaches to the shortest common supersequence problem. In: Cabestany, J., Prieto, A.G., Sandoval, F. (eds.) IWANN 2005, vol. 3512, pp. 50–58. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Ford Jr., L.R., Fulkerson, D.R.: Flows in networks, Princeton, N.Y (1962)

    Google Scholar 

  6. Fraser, C.B., Irving, R.W.: Approximation alrorithms for the shortest common supersequence. Nordic J. Comput. 2(3), 303–325 (1995)

    MathSciNet  MATH  Google Scholar 

  7. Gusfield, D.: Efficient methods for multiple sequence alignment with guaranteed error bounds. Bull. Math. Biol. 55(1), 141–154 (1993)

    Article  MATH  Google Scholar 

  8. Jiang, T., Li, M.: On the approximation of shortest common supersequences and longest common subsequences. SIAM J. on Discrete Math. (1992)

    Google Scholar 

  9. Maier, D.: The complexity of some problems on subsequences and supersequences. J. ACM 25, 322–336 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  10. Middendorf, M.: The shortest common non-subsequence problem is NP-complete. Theoret. Comput. Sci. 108, 365–369 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ning, K., Leong, H.W.: Towards a better solution to the schortest common supersequence problem: the decomposition and reduction algorithm. BMC Bioinformatics 7(suppl. 4), S12 (2006)

    Article  Google Scholar 

  12. Pevzner, P.A.: Multiple alignment, communication costs, and graph matching. SIAM J. on Appl. Math. 52, 1763–1779 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  13. Pietrzak, K.: On the parameterized complexity of the fixed alphabet shortest common supersequence and longest common subsequence problems. J. Comput. System Sci. 67, 757–771 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. Raiha, K.-J., Ukkonen, E.: The shortest common supersequence problem over binary alphabet is NP-complete. Theoret. Comput. Sci. 16, 187–198 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  15. Reingold, E.M., Nievergelt, J., Deo, N.: Combinatorial algorithms. Prentice-Hall, Inc., Englewood Cliffs (1977)

    MATH  Google Scholar 

  16. Rubinov, A.R., Timkovsky, V.G.: Nonsimilarity combinatorial problems. BioSystems 30, 81–92 (1993); Pevzner, P.A., Gelfand, M.S. (eds.): Computer Genetics, pp. 81–92. Elsevier (1993)

    Google Scholar 

  17. Rubinov, A.R., Timkovsky, V.G.: String noninclusion optimization problems. SIAM J. Discrete Math. 11, 456–467 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  18. Sankoff, D.: Minimum mutation tree of sequences. SIAM J. Appl. Math. 28, 35–42 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  19. Timkovsky, V.G.: Complexity of common subsequnce and supersequence problems and related problems. Kibernetika 5, 1–13 (1989); Cybernetics 25, 565–580 (1990) (English translation)

    Google Scholar 

  20. Waterman, M.S., Smith, T.F., Beyer, W.A.: Some biological sequence metrics. Adv. Math. 20, 367–387 (1976)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Economics and Business, The University of Sydney, NSW 2006, Australia

    Vadim G. Timkovsky

Authors
  1. Vadim G. Timkovsky
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Bar-Ilan University, 52900, Ramat-Gan, Israel

    Amihood Amir

  2. School of Computer Science and Information Technology, RMIT University, Melbourne, Australia

    Andrew Turpin

  3. NICTA Victoria Laboratory, Department of Computer Science and Software Engineering, The University of Melbourne, Victoria, Australia

    Alistair Moffat

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© 2008 Springer-Verlag Berlin Heidelberg

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Timkovsky, V.G. (2008). Some Approximations for Shortest Common Nonsubsequences and Supersequences. In: Amir, A., Turpin, A., Moffat, A. (eds) String Processing and Information Retrieval. SPIRE 2008. Lecture Notes in Computer Science, vol 5280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89097-3_25

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  • DOI: https://doi.org/10.1007/978-3-540-89097-3_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89096-6

  • Online ISBN: 978-3-540-89097-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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