Parameterized Complexity and Kernelizability of Max Ones and Exact Ones Problems [chapter]

Stefan Kratsch, Dániel Marx, Magnus Wahlström
2010 Lecture Notes in Computer Science  
For a finite set Γ of Boolean relations, Max Ones SAT(Γ ) and Exact Ones SAT(Γ ) are generalized satisfiability problems where every constraint relation is from Γ , 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(Γ ), we give a classification into 5 different complexity levels: polynomial-time solvable,
more » ... dmits a polynomial kernel, fixed-parameter tractable, solvable in polynomial time for fixed k, and NP-hard already for k = 1. For Exact Ones SAT(Γ ), we refine the classification obtained earlier by having a closer look at the fixed-parameter tractable cases and classifying the sets Γ for which Exact Ones SAT(Γ ) admits a polynomial kernel.
doi:10.1007/978-3-642-15155-2_43 fatcat:nuloby4el5agdil6gaq6dtgnhq