Abstract.
We prove a parameterized analog of Schaefer’s Dichotomy Theorem: we show that for every finite boolean constraint family ℱ, deciding whether a formula containing constraints from ℱ has a satisfying assignment of weight exactly k is either fixed-parameter tractable (FPT) or W[1]-complete. We give a simple characterization of those constraints that make the problem fixed-parameter tractable. The special cases when the formula is restricted to be bounded occurrence, bounded treewidth, or planar are also considered: it turns out that in these cases the problem is in FPT for every constraint family ℱ.
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Manuscript received 30 September 2004
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Marx, D. Parameterized complexity of constraint satisfaction problems. comput. complex. 14, 153–183 (2005). https://doi.org/10.1007/s00037-005-0195-9
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DOI: https://doi.org/10.1007/s00037-005-0195-9