Exact Solutions for Closest String and Related Problems

  • Jens Gramm
  • Rolf Niedermeier
  • Peter Rossmanith
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2223)


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 same length and a positive integer d, find a “closest string” s such that none of the given strings has Hamming distance greater than d from s. Closest String is NP-complete. We show how to solve CLOSEST STRING in linear time for constant d (the exponential growth is O(d d . We extend this result to the closely related problems d-MISMATCH and DISTINGUISHING STRING SELECTION. Moreover, we discuss fixed parameter tractability for parameter k and give an efficient linear time algorithm for CLOSEST STRING when k = 3. Finally, the practical usefulness of our findings is substantiated by some experimental results.


Linear Time Search Tree Majority Vote Close String Input String 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Jens Gramm
    • 1
  • Rolf Niedermeier
    • 1
  • Peter Rossmanith
    • 2
  1. 1.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenGermany
  2. 2.Institut für InformatikTechnische Universität MünchenMünchenGermany

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