Parameterized complexity of constraint satisfaction problems

Authors:
Dániel Marx
Affiliations:
Department of Computer Science and Information Theory, Budapest University of Technology and Economics, Budapest, Hungary H-1521
Venue:
Computational Complexity
Year:
2005

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Abstract

We prove a parameterized analog of Schaefer's Dichotomy Theorem: we show that for every finite boolean constraint family 驴, deciding whether a formula containing constraints from 驴 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 驴.