Finding Consensus Strings with Small Length Difference Between Input and Solution Strings

  • Markus L. Schmid
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9235)


The parameterised complexity of the Closest Substring Problem and the Consensus Patterns Problem with respect to the parameter \((\ell - m)\) is investigated, where \(\ell \) is the maximum length of the input strings and m is the length of the solution string. We present an exact exponential time algorithm for both problems, which is based on an alphabet reduction. Furthermore, it is shown that for most combinations of \((\ell - m)\) and one of the classical parameters (m, \(\ell \), number of input strings k, distance d), we obtain fixed-parameter tractability, but even for constant \((\ell - m)\) and constant alphabet size, both problems are \({{\mathrm{\mathsf {NP}}}}\)-hard.


Parameterised complexity Hard string problems 


  1. 1.
    Bulteau, L., Hüffner, F., Komusiewicz, C., Niedermeier, R.: Multivariate algorithmics for np-hard string problems. EATCS Bull. 114, 31–73 (2014)Google Scholar
  2. 2.
    Evans, P.A., Smith, A.D., Wareham, H.T.: On the complexity of finding common approximate substrings. Theoret. Comput. Sci. 306, 407–430 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Fellows, M.R., Gramm, J., Niedermeier, R.: On the parameterized intractability of motif search problems. Combinatorica 26, 141–167 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer-Verlag, New York (2006)zbMATHGoogle Scholar
  5. 5.
    Frances, M., Litman, A.: On covering problems of codes. Theor. Comput. Sys. 30, 113–119 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Gramm, J., Niedermeier, R., Rossmanith, P.: Fixed-parameter algorithms for closest string and related problems. Algorithmica 37, 25–42 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Kratochvíl, J., Kr̆ivánek, M.: On the computational complexity of codes in graphs. In: Chytil, M.P., Koubek, V., Janiga, L. (eds.) Mathematical Foundations of Computer Science 1988. LNCS, pp. 396–404. Springer, Heidelberg (1988)CrossRefGoogle Scholar
  8. 8.
    Marx, D.: Closest substring problems with small distances. SIAM J. Comput. 38, 1382–1410 (2008)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Trier University, Fachbereich IV – Abteilung InformatikwissenschaftenTrierGermany

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