, Volume 74, Issue 1, pp 540–557 | Cite as

Backdoors to q-Horn

  • Serge Gaspers
  • Sebastian Ordyniak
  • M. S. Ramanujan
  • Saket Saurabh
  • Stefan Szeider


The class \(\text {q-Horn}\), introduced by Boros, Crama and Hammer in 1990, is one of the largest known classes of propositional CNF formulas for which satisfiability can be decided in polynomial time. This class properly contains the fundamental classes of Horn and 2-CNF formulas as well as the class of renamable (or disguised) Horn formulas. In this paper we extend this class so that its favorable algorithmic properties can be made accessible to formulas that are outside but “close” to this class. We show that deciding satisfiability is fixed-parameter tractable parameterized by the distance of the given formula from \(\text {q-Horn}\). The distance is measured by the smallest number of variables that we need to delete from the formula in order to get a \(\text {q-Horn}\) formula, i.e., the size of a smallest deletion backdoor set into the class \(\text {q-Horn}\). This result generalizes known fixed-parameter tractability results for satisfiability decision with respect to the parameters distance from Horn, 2-CNF, and renamable Horn.


Algorithms and data structures Backdoor sets Satisfiability Fixed parameter tractability 



The authors acknowledge support from the OeAD (Austrian Indian collaboration grant, IN13/2011). Serge Gaspers, Sebastian Ordyniak, and Stefan Szeider acknowledge support from the European Research Council (COMPLEX REASON, 239962) and Serge Gaspers acknowledges support from the Australian Research Council (DE120101761).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Serge Gaspers
    • 1
    • 2
  • Sebastian Ordyniak
    • 3
  • M. S. Ramanujan
    • 4
  • Saket Saurabh
    • 4
  • Stefan Szeider
    • 5
  1. 1.The University of New South WalesSydneyAustralia
  2. 2.National ICT AustraliaSydneyAustralia
  3. 3.Masaryk UniversityBrnoCzech Republic
  4. 4.The Institute of Mathematical SciencesChennaiIndia
  5. 5.Institute of Information SystemsVienna University of TechnologyViennaAustria

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