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Exact Solutions for Closest String and Related Problems

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Algorithms and Computation (ISAAC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2223))

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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 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.

Supported by the Deutsche Forschungsgemeinschaft (DFG), project OPAL (optimal solutions for hard problems in computational biology), NI 369/2-1.

Frances and Litman [4] show the NP-completeness of Closest String, considering it from the viewpoint of coding theory (so-called Minimum Radius problem).

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Author information

Authors and Affiliations

  1. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076, Tübingen, Germany

    Jens Gramm & Rolf Niedermeier

  2. Institut für Informatik, Technische Universität München, Arcisstr. 21, D-80290, München, Germany

    Peter Rossmanith

Authors
  1. Jens Gramm
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  2. Rolf Niedermeier
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  3. Peter Rossmanith
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Editor information

Editors and Affiliations

  1. Basser Department of Computer Science, University of Sydney, Madsen Building F09, 2006, Sydney, NSW, Australia

    Peter Eades

  2. Department of Computer Science, University of Canterbury, Private Bag 4800, Christchurch, New Zealand

    Tadao Takaoka

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© 2001 Springer-Verlag Berlin Heidelberg

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Gramm, J., Niedermeier, R., Rossmanith, P. (2001). Exact Solutions for Closest String and Related Problems. In: Eades, P., Takaoka, T. (eds) Algorithms and Computation. ISAAC 2001. Lecture Notes in Computer Science, vol 2223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45678-3_38

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  • DOI: https://doi.org/10.1007/3-540-45678-3_38

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42985-2

  • Online ISBN: 978-3-540-45678-0

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