Algorithmica

, Volume 37, Issue 1, pp 25–42 | Cite as

Fixed-Parameter Algorithms for CLOSEST STRING and Related Problems

  • Gramm
  • Niedermeier
  • Rossmanith
Article

Abstract

CLOSEST STRING is one of the core problems in the field of consensus word analysis with particular importance for computational biology. Given k strings of the same length and a nonnegative integer d , find a ``center string'' s such that none of the given strings has the Hamming distance greater than d from s . CLOSEST STRING is NP-complete. In biological applications, however, d is usually very small. We show how to solve CLOSEST STRING in linear time for fixed d —the exponential growth in d is bounded by O(dd) . We extend this result to the closely related problems d -MISMATCH and DISTINGUISHING STRING SELECTION. Moreover, we also show that CLOSEST STRING is solvable in linear time when k is fixed and d is arbitrary. In summary, this means that CLOSEST STRING is fixed-parameter tractable with respect to parameter d and with respect to parameter k . Finally, the practical usefulness of our findings is substantiated by some experimental results.

Keywords

Consensus word analysis NP-complete Exact algorithms Fixed-parameter tractability 

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Copyright information

© Springer-Verlag New York 2003

Authors and Affiliations

  • Gramm
    • 1
  • Niedermeier
    • 1
  • Rossmanith
    • 2
  1. 1.Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076 Tübingen, Germany. gramm@informatik.uni-tuebingen.de, niedermr@informatik.uni-tuebingen.de.DE
  2. 2.Lehrgebiet Theoretische Informatik, RWTH Aachen, Ahornstraß e 55, D-52056 Aachen, Germany. rossmani@informatik.rwth-aachen.de.DE

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