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Restricted and Swap Common Superstring: A Parameterized View

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7535)

Abstract

In several areas, in particular in bioinformatics and in AI planning, Shortest Common Superstring problem (SCS) and variants thereof have been successfully applied. In this paper we consider two variants of SCS recently introduced (Restricted Common Superstring, \(\ensuremath{\text{\textsc{RCS}}}\)) and (Swapped Common Superstring, \(\ensuremath{\text{\textsc{SWCS}}}\)). In \(\ensuremath{\text{\textsc{RCS}}}\) we are given a set S of strings and a multiset, and we look for an ordering \(\mathcal{M}_o\) of \(\mathcal{M}\) such that the number of input strings which are substrings of \(\mathcal{M}_o\) is maximized. In \(\ensuremath{\text{\textsc{SWCS}}}\) we are given a set S of strings and a text \(\mathcal{T}\), and we look for a swap ordering \(\mathcal{T}_o\) of \(\mathcal{T}\) (an ordering of \(\mathcal{T}\) obtained by swapping only some pairs of adjacent characters) such that the number of input strings which are substrings of \(\mathcal{T}_o\) is maximized. In this paper we investigate the parameterized complexity of the two problems. We give two fixed-parameter algorithms, where the parameter is the size of the solution, for \(\ensuremath{\text{\textsc{SWCS}}}\) and \(\ensuremath{\text{\textsc{$\ell$-RCS}}} \) (the \(\ensuremath{\text{\textsc{RCS}}}\) problem restricted to strings of length bounded by a parameter ℓ). Furthermore, we complement these results by showing that \(\ensuremath{\text{\textsc{SWCS}}}\) and \(\ensuremath{\text{\textsc{$\ell$-RCS}}} \) do not admit a polynomial kernel.

Keywords

  • Polynomial Time
  • Hash Function
  • Parameterized Complexity
  • Polynomial Kernel
  • Simple Path

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bonizzoni, P., Dondi, R., Mauri, G., Zoppis, I. (2012). Restricted and Swap Common Superstring: A Parameterized View. In: Thilikos, D.M., Woeginger, G.J. (eds) Parameterized and Exact Computation. IPEC 2012. Lecture Notes in Computer Science, vol 7535. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33293-7_7

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  • DOI: https://doi.org/10.1007/978-3-642-33293-7_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33292-0

  • Online ISBN: 978-3-642-33293-7

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