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Parameterized Complexity of Superstring Problems

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Combinatorial Pattern Matching (CPM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9133))

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Abstract

In the Shortest Superstring problem we are given a set of strings \(S=\{s_1, \ldots , s_n\}\) and an integer \(\ell \) and the question is to decide whether there is a superstring \(s\) of length at most \(\ell \) containing all strings of \(S\) as substrings. We obtain several parameterized algorithms and complexity results for this problem.

In particular, we give an algorithm which in time \(2^{O(k)} {\text {poly}}(n)\) finds a superstring of length at most \(\ell \) containing at least \(k\) strings of \(S\). We complement this by the lower bound showing that such a parameterization does not admit a polynomial kernel up to some complexity assumption. We also obtain several results about “below guaranteed values” parameterization of the problem. We show that parameterization by compression admits a polynomial kernel while parameterization “below matching” is hard.

The research leading to these results has received funding from the Government of the Russian Federation (grant 14.Z50.31.0030) and Grant of the President of Russian Federation (MK-6550.2015.1).

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Author information

Authors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Fedor V. Fomin, Petr A. Golovach & Saket Saurabh

  2. Steklov Institute of Mathematics at St. Petersburg, Russian Academy of Sciences, St. Petersburg, Russia

    Ivan Bliznets, Fedor V. Fomin, Petr A. Golovach, Nikolay Karpov & Alexander S. Kulikov

  3. Institute of Mathematical Sciences, Chennai, India

    Saket Saurabh

Authors
  1. Ivan Bliznets
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  2. Fedor V. Fomin
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  3. Petr A. Golovach
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  4. Nikolay Karpov
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  5. Alexander S. Kulikov
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  6. Saket Saurabh
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Corresponding author

Correspondence to Petr A. Golovach .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Verona, Verona, Italy

    Ferdinando Cicalese

  2. Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel

    Ely Porat

  3. Department of Computer Science, University of Salerno, Fisciano, Italy

    Ugo Vaccaro

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Bliznets, I., Fomin, F.V., Golovach, P.A., Karpov, N., Kulikov, A.S., Saurabh, S. (2015). Parameterized Complexity of Superstring Problems. In: Cicalese, F., Porat, E., Vaccaro, U. (eds) Combinatorial Pattern Matching. CPM 2015. Lecture Notes in Computer Science(), vol 9133. Springer, Cham. https://doi.org/10.1007/978-3-319-19929-0_8

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  • DOI: https://doi.org/10.1007/978-3-319-19929-0_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19928-3

  • Online ISBN: 978-3-319-19929-0

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