A Subexponential Parameterized Algorithm for Proper Interval Completion

  • Ivan Bliznets
  • Fedor V. Fomin
  • Marcin Pilipczuk
  • Michał Pilipczuk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8737)


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.


Interval Graph Polynomial Kernel Chordal Graph Graph Class Completion Problem 
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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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

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