The Approximability of Constraint Satisfaction Problems
SIAM Journal on Computing
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Infeasibility of instance compression and succinct PCPs for NP
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Parameterized complexity of constraint satisfaction problems
Computational Complexity
Exact Algorithms for Exact Satisfiability and Number of Perfect Matchings
Algorithmica - Parameterized and Exact Algorithms
On Problems without Polynomial Kernels (Extended Abstract)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
A quadratic kernel for feedback vertex set
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Boolean Constraint Satisfaction Problems: When Does Post's Lattice Help?
Complexity of Constraints
A Problem Kernelization for Graph Packing
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Two Edge Modification Problems without Polynomial Kernels
Parameterized and Exact Computation
A cubic kernel for feedback vertex set
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses
Proceedings of the forty-second ACM symposium on Theory of computing
On the Compressibility of $\mathcal{NP}$ Instances and Cryptographic Applications
SIAM Journal on Computing
The undirected feedback vertex set problem has a poly(k) kernel
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Kernelization algorithms for d-hitting set problems
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Parameterized Complexity
Parameterized complexity and kernelizability of max ones and exact ones problems
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Solving MINONES-2-SAT as fast as VERTEX COVER
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Constraint satisfaction parameterized by solution size
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
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
Co-nondeterminism in compositions: a kernelization lower bound for a Ramsey-type problem
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Discrete Optimization
Instance compression for the polynomial hierarchy and beyond
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Solving min ones 2-sat as fast as vertex cover
Theoretical Computer Science
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Min Ones Constraint Satisfaction Problems, i.e., the task of finding a satisfying assignment with at most k true variables (Min Ones SAT(Γ)), can express a number of interesting and natural problems. We study the preprocessing properties of this class of problems with respect to k, using the notion of kernelization to capture the viability of preprocessing. We give a dichotomy of Min Ones SAT(Γ) problems into admitting or not admitting a kernelization with size guarantee polynomial in k, based on the constraint language Γ. We introduce a property of boolean relations called mergeability that can be easily checked for any Γ. When all relations in Γ are mergeable, then we show a polynomial kernelization for Min Ones SAT(Γ). Otherwise, any Γ containing a non-mergeable relation and such that Min Ones SAT(Γ) is NP-complete permits us to prove thatMin Ones SAT(Γ) does not admit a polynomial kernelization unless NP ⊆ co-NP/poly, by a reduction from a particular parameterization of Exact Hitting Set.