Parameterized Complexity of Superstring Problems

  • Ivan Bliznets
  • Fedor V. Fomin
  • Petr A. GolovachEmail author
  • Nikolay Karpov
  • Alexander S. Kulikov
  • Saket Saurabh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9133)


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.


Directed Graph Undirected Graph Parameterized Complexity Vertex Cover Parameterized Problem 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Ivan Bliznets
    • 2
  • Fedor V. Fomin
    • 1
    • 2
  • Petr A. Golovach
    • 1
    • 2
    Email author
  • Nikolay Karpov
    • 2
  • Alexander S. Kulikov
    • 2
  • Saket Saurabh
    • 1
    • 3
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.Steklov Institute of Mathematics at St. PetersburgRussian Academy of SciencesSt. PetersburgRussia
  3. 3.Institute of Mathematical SciencesChennaiIndia

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