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On Approximating String Selection Problems with Outliers

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Combinatorial Pattern Matching (CPM 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7354))

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Abstract

Many problems in bioinformatics are about finding strings that approximately represent a collection of given strings. We look at more general problems where some input strings can be classified as outliers. The Close to Most Strings problem is, given a set S of same-length strings, and a parameter d, find a string x that maximizes the number of “non-outliers” within Hamming distance d of x. We prove that this problem has no polynomial-time approximation scheme (PTAS) unless NP has randomized polynomial-time algorithms, correcting a decade-old mistake. The Most Strings with Few Bad Columns problem is to find a maximum-size subset of input strings so that the number of non-identical positions is at most k; we show it has no PTAS unless P=NP. We also observe Closest to k Strings has no efficient PTAS (EPTAS) unless the parameterized complexity hierarchy collapses. In sum, outliers help model problems associated with using biological data, but we show the problem of finding an approximate solution is computationally difficult.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of California, San Diego, USA

    Christina Boucher

  2. Department of Computer Science, University of Haifa, Haifa, 31905, Israel

    Gad M. Landau & Oren Weimann

  3. Polytechnic Institute of NYU, Brooklyn, NY, 11201-3840, USA

    Gad M. Landau

  4. Shenkar College for Engineering and Design, Ramat-Gan, Israel

    Avivit Levy

  5. CRI, University of Haifa, Mount Carmel, Haifa, 31905, Israel

    Avivit Levy

  6. CEMC, University of Waterloo, Canada

    David Pritchard

Authors
  1. Christina Boucher
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  2. Gad M. Landau
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  3. Avivit Levy
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  4. David Pritchard
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  5. Oren Weimann
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Helsinki, Gustaf Hällström Katu 2b, P.O. Box 68, 00014, Helsinki, Finland

    Juha Kärkkäinen

  2. Faculty of Technology, University of Bielefeld, Universitätsstraße 25, 33615, Bielefeld, Germany

    Jens Stoye

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© 2012 Springer-Verlag Berlin Heidelberg

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Boucher, C., Landau, G.M., Levy, A., Pritchard, D., Weimann, O. (2012). On Approximating String Selection Problems with Outliers. In: Kärkkäinen, J., Stoye, J. (eds) Combinatorial Pattern Matching. CPM 2012. Lecture Notes in Computer Science, vol 7354. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31265-6_34

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  • DOI: https://doi.org/10.1007/978-3-642-31265-6_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31264-9

  • Online ISBN: 978-3-642-31265-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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