We present a randomized subexponential time, polynomial space parameterized algorithm for the k -Weighted Feedback Arc Set in Tournaments (k -FAST) problem. We also show that our algorithm can be derandomized by slightly increasing the running time. To derandomize our algorithm we construct a new kind of universal hash functions, that we coin universal coloring families. For integers m,k and r, a family \({\mathcal F}\) of functions from [m] to [r] is called a universal (m,k,r)-coloring family if for any graph G on the set of vertices [m] with at most k edges, there exists an \(f \in {\mathcal F}\) which is a proper vertex coloring of G. Our algorithm is the first non-trivial subexponential time parameterized algorithm outside the framework of bidimensionality.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Noga Alon
    • 1
    • 2
  • Daniel Lokshtanov
    • 3
  • Saket Saurabh
    • 3
  1. 1.Tel Aviv UniversityTel AvivIsrael
  2. 2.IASPrincetonUSA
  3. 3.Department of InformaticsUniversity of BergenBergenNorway

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