Algorithmica

, Volume 79, Issue 3, pp 798–813 | Cite as

Parameterized Complexity of Superstring Problems

  • Ivan Bliznets
  • Fedor V. Fomin
  • Petr A. Golovach
  • Nikolay Karpov
  • Alexander S. Kulikov
  • Saket Saurabh
Article
  • 109 Downloads

Abstract

In the Shortest Superstring problem we are given a set of strings \(S=\{s_1, \ldots , s_n\}\) and 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 \(2^{\mathcal {O}(k)} {\text {poly}}(n)\) finds a superstring of length at most \(\ell \) containing at least k strings of S. We complement this by a 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.

Keywords

Shortest superstring Parameterized complexity Kernelization 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Ivan Bliznets
    • 1
  • Fedor V. Fomin
    • 1
    • 2
  • Petr A. Golovach
    • 1
    • 2
  • Nikolay Karpov
    • 1
  • Alexander S. Kulikov
    • 1
  • Saket Saurabh
    • 2
    • 3
  1. 1.St. Petersburg Department of Steklov Institute of Mathematics of the Russian Academy of SciencesSaint PetersburgRussia
  2. 2.Department of InformaticsUniversity of BergenBergenNorway
  3. 3.Institute of Mathematical SciencesChennaiIndia

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