computational complexity

, Volume 14, Issue 2, pp 153–183 | Cite as

Parameterized complexity of constraint satisfaction problems

Open Access
Original Paper


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.


Constraint satisfaction weighted satisfiability parameterized complexity weak separability 

Subject classification.

68Q25 68Q17 

Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Department of Computer Science and Information TheoryBudapest University of Technology and EconomicsBudapestHungary

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