A Subexponential Parameterized Algorithm for Proper Interval Completion

  • Ivan Bliznets
  • Fedor V. Fomin
  • Marcin Pilipczuk
  • Michał Pilipczuk
Conference paper

DOI: 10.1007/978-3-662-44777-2_15

Volume 8737 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Bliznets I., Fomin F.V., Pilipczuk M., Pilipczuk M. (2014) A Subexponential Parameterized Algorithm for Proper Interval Completion. In: Schulz A.S., Wagner D. (eds) Algorithms - ESA 2014. ESA 2014. Lecture Notes in Computer Science, vol 8737. Springer, Berlin, Heidelberg

Abstract

In the Proper Interval Completion problem we are given a graph G and an integer k, and the task is to turn G using at most k edge additions into a proper interval graph, i.e., a graph admitting an intersection model of equal-length intervals on a line. The study of Proper Interval Completion from the viewpoint of parameterized complexity has been initiated by Kaplan, Shamir and Tarjan [FOCS 1994; SIAM J. Comput. 1999], who showed an algorithm for the problem working in \(\mathcal{O}(16^k\cdot (n+m))\) time. In this paper we present an algorithm with running time \(k^{\mathcal{O}(k^{2/3})} + \mathcal{O}(nm(kn+m))\), which is the first subexponential parameterized algorithm for Proper Interval Completion.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Ivan Bliznets
    • 1
  • Fedor V. Fomin
    • 1
    • 2
  • Marcin Pilipczuk
    • 2
  • Michał Pilipczuk
    • 2
  1. 1.St. Petersburg Department of SteklovInstitute of MathematicsRussia
  2. 2.Department of InformaticsUniversity of BergenNorway