On the Longest Common Parameterized Subsequence

  • Orgad Keller
  • Tsvi Kopelowitz
  • Moshe Lewenstein
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5029)


The well-known problem of the longest common subsequence (LCS), of two strings of lengths n and m respectively, is O(nm)-time solvable and is a classical distance measure for strings. Another well-studied string comparison measure is that of parameterized matching, where two equal-length strings are a parameterized-match if there exists a bijection on the alphabets such that one string matches the other under the bijection. All works associated with parameterized pattern matching present polynomial time algorithms.

There have been several attempts to accommodate parameterized matching along with other distance measures, as these turn out to be natural problems, e.g., Hamming distance, and a bounded version of edit-distance. Several algorithms have been proposed for these problems.

In this paper we consider the longest common parameterized subsequence problem which combines the LCS measure with parameterized matching. We prove that the problem is NP-hard, and then show a couple of approximation algorithms for the problem.


Input String Type Edge Longe Common Subsequence Sequence Graph Longe Common Subsequence 
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  1. 1.
    Amir, A., Farach, M., Muthukrishnan, S.: Alphabet dependence in parameterized matching. Inf. Process. Lett. 49(3), 111–115 (1994)zbMATHCrossRefGoogle Scholar
  2. 2.
    Baker, B.S.: Parameterized pattern matching by boyer-moore-type algorithms. In: SODA, pp. 541–550 (1995)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, B.S.: Parameterized duplication in strings: Algorithms and an application to software maintenance. SIAM J. Comput. 26(5), 1343–1362 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Baker, B.S.: Parameterized diff. In: SODA, pp. 854–855 (1999)Google Scholar
  6. 6.
    Cole, R., Hariharan, R.: Faster suffix tree construction with missing suffix links. In: STOC, pp. 407–415 (2000)Google Scholar
  7. 7.
    Ferragina, F., Grossi, R.: The string b-tree: A new data structure for string search in external memory and its applications. J. ACM 46(2), 236–280 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Hazay, C., Lewenstein, M., Sokol, D.: Approximate parameterized matching. ACM Transactions on Algorithms 3(3) (2007)Google Scholar
  9. 9.
    Hazay, C., Lewenstein, M., Tsur, D.: Two dimensional parameterized matching. In: Apostolico, A., Crochemore, M., Park, K. (eds.) CPM 2005. LNCS, vol. 3537, pp. 266–279. Springer, Heidelberg (2005)Google Scholar
  10. 10.
    Hunt, J.W., Szymanski, T.G.: A fast algorithm for computing longest subsequences. Commun. ACM 20(5), 350–353 (1977)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Jiang, T., Li, M.: On the approximation of shortest common supersequences and longest common subsequences. SIAM J. Comput. 24(5), 1122–1139 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Karp, R.M.: Reducibility among combinatorial problems. In: Complexity of Computer Computations, pp. 85–103. Plenum Press (1972)Google Scholar
  13. 13.
    Kosaraju, S.R.: Faster algorithms for the construction of parameterized suffix trees (preliminary version). In: FOCS, pp. 631–637 (1995)Google Scholar
  14. 14.
    Levenshtein, V.I.: Binary codes capable of correcting deletions, insertions, and reversals. Soviet Physics Doklady 10, 707–710 (1966)MathSciNetGoogle Scholar
  15. 15.
    Maier, D.: The complexity of some problems on subsequences and supersequences. J. ACM 25(2), 322–336 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Masek, W.J., Paterson, M.: A faster algorithm computing string edit distances. J. Comput. Syst. Sci. 20(1), 18–31 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Myers, E.W.: An o(nd) difference algorithm and its variations. Algorithmica 1(2), 251–266 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Nakatsu, N., Kambayashi, Y., Yajima, S.: A longest common subsequence algorithm suitable for similar text strings. Acta Inf. 18, 171–179 (1982)zbMATHMathSciNetGoogle Scholar
  19. 19.
    Wagner, R.A., Fischer, M.J.: The string-to-string correction problem. J. ACM 21(1), 168–173 (1974)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Orgad Keller
    • 1
  • Tsvi Kopelowitz
    • 1
  • Moshe Lewenstein
    • 1
  1. 1.Department of Computer ScienceBar-Ilan UniversityRamat-GanIsrael

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