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On the Parameterized Intractability of Closest Substring and Related Problems

  • Michael R. Fellows
  • Jens Gramm
  • Rolf Niedermeier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2285)

Abstract

We show that Closest Substring, one of the most important problems in the field of biological sequence analysis, is W[1]-hard with respect to the number k of input strings (even over a binary alphabet). This problem is therefore unlikely to be solvable in time O(f(k)n c) for any function fand constant c independent of k— effectively, the problem can be expected to be intractable, in any practical sense, for k ≥ 3. Our result supports the intuition that Closest Substring is computationally much harder than the special case of Closest String, although both problems are NP-complete and both possess polynomial time approximation schemes. We also prove W[1]-hardness for other parameterizations in the case of unbounded alphabet size. Our main W[1]- hardness result generalizes to CONSENSUS PATTERNS, a problem of similar significance in computational biology.

Keywords

Close String Vertex Cover Input Graph Solution String Input String 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Michael R. Fellows
    • 1
  • Jens Gramm
    • 2
  • Rolf Niedermeier
    • 2
  1. 1.Department of Computer Science and Software EngineeringUniversity of Newcastle, University DriveCallaghanAustralia
  2. 2.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenFed. Rep. of Germany

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