Parameterized Complexity and Kernelizability of Max Ones and Exact Ones Problems

  • Stefan Kratsch
  • Dániel Marx
  • Magnus Wahlström
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6281)


For a finite set \(\it\Gamma\) of Boolean relations, Max Ones SAT(\(\it\Gamma\)) and Exact Ones SAT(\(\it\Gamma\)) are generalized satisfiability problems where every constraint relation is from \(\it\Gamma\), and the task is to find a satisfying assignment with at least/exactly k variables set to 1, respectively. We study the parameterized complexity of these problems, including the question whether they admit polynomial kernels. For Max Ones SAT(\(\it\Gamma\)), we give a classification into 5 different complexity levels: polynomial-time solvable, admits a polynomial kernel, fixed-parameter tractable, solvable in polynomial time for fixed k, and NP-hard already for k = 1. For Exact Ones SAT(\(\it\Gamma\)), we refine the classification obtained earlier by having a closer look at the fixed-parameter tractable cases and classifying the sets \(\it\Gamma\) for which Exact Ones SAT(\(\it\Gamma\)) admits a polynomial kernel.


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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Stefan Kratsch
    • 1
  • Dániel Marx
    • 2
  • Magnus Wahlström
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany
  2. 2.Tel Aviv UniversityIsrael

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