When Is Weighted Satisfiability FPT?

  • Iyad A. Kanj
  • Ge Xia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8037)


The weighted monotone and antimonotone satisfiability problems on normalized circuits, abbreviated wsat  + [t] and wsat [t], are canonical problems in the parameterized complexity theory. We study the parameterized complexity of wsat [t] and wsat  + [t], where t ≥ 2, with respect to the genus of the circuit. For wsat [t], we give a fixed-parameter tractable (FPT) algorithm when the genus of the circuit is n o(1), where n is the number of the variables in the circuit. For wsat  + [2] (i.e., weighted monotone cnf-sat) and wsat  + [3], which are both W[2]-complete, we also give FPT algorithms when the genus is n o(1). For wsat  + [t] where t > 3, we give FPT algorithms when the genus is \(O(\sqrt{\log{n}})\). We also show that both wsat [t] and wsat  + [t] on circuits of genus n Ω(1) have the same W-hardness as the general wsat  + [t] and wsat [t] problem (i.e., with no restriction on the genus), thus drawing a precise map of the parameterized complexity of wsat [t], and of wsat  + [t], for t = 2,3, with respect to the genus of the underlying circuit.

As a byproduct of our results, we obtain, via standard parameterized reductions, tight results on the parameterized complexity of several problems with respect to the genus of the underlying graph.


Parameterized Complexity Tree Decomposition Truth Assignment Satisfying Assignment Underlying Graph 
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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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Iyad A. Kanj
    • 1
  • Ge Xia
    • 2
  1. 1.School of ComputingDePaul UniversityChicagoUSA
  2. 2.Dept. of Computer ScienceLafayette CollegeEastonUSA

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