On the Structure of Polynomial Time Reducibility
Journal of the ACM (JACM)
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
The Approximability of Constraint Satisfaction Problems
SIAM Journal on Computing
On the Hamming distance of constraint satisfaction problems
Theoretical Computer Science - Complexity and logic
A Dichotomy Theorem for Constraints on a Three-Element Set
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Tractable conservative Constraint Satisfaction Problems
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized complexity of constraint satisfaction problems
Computational Complexity
On Problems without Polynomial Kernels (Extended Abstract)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Non-uniform Boolean Constraint Satisfaction Problems with Cardinality Constraint
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Finding paths of length k in O∗(2k) time
Information Processing Letters
Frozen Boolean Partial Co-clones
ISMVL '09 Proceedings of the 2009 39th International Symposium on Multiple-Valued Logic
Preprocessing of min ones problems: a dichotomy
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Parameterized Complexity
Kernelization of packing problems
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Weak compositions and their applications to polynomial lower bounds for kernelization
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Kernels for packing and covering problems
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
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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, 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(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.