Kratsch, S and Marx, Dániel and Wahlstrom, M (2016) Parameterized Complexity and Kernelizability of Max Ones and Exact Ones Problems. ACM Transactions on Computation Theory, 8 (1). p. 1. ISSN 1942-3454 10.1145/2858787

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Abstract

For a finite set Gamma of Boolean relations, MAX ONES SAT(Gamma) and EXACT ONES SAT(Gamma) are generalized satisfiability problems where every constraint relation is from 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(Gamma), we give a classification into five 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(Gamma), we refine the classification obtained earlier by taking a closer look at the fixed-parameter tractable cases and classifying the sets Gamma for which EXACT ONES SAT(Gamma) admits a polynomial kernel.

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