The Minimum Satisfiability Problem
SIAM Journal on Discrete Mathematics
Polynomial time approximation schemes for dense instances of NP-hard problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
MAX-CUT has a randomized approximation scheme in dense graphs
Random Structures & Algorithms
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
On the approximation hardness of dense TSP and other path problems
Information Processing Letters
Polynomial time approximation of dense weighted instances of MAX-CUT
Random Structures & Algorithms
Approximating minimum unsatisfiability of linear equations
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
On Dependent Randomized Rounding Algorithms
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Approximability of Dense Instances of NEAREST CODEWORD Problem
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Improved Non-approximability Results for Vertex Cover with Density Constraints
COCOON '96 Proceedings of the Second Annual International Conference on Computing and Combinatorics
Polynominal Time Approximation Schemes for Some Dense Instances of NP-Hard Optimization Problems
RANDOM '97 Proceedings of the International Workshop on Randomization and Approximation Techniques in Computer Science
Constraint Satisfaction: The Approximability of Minimization Problems
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
Approximating-CVP to within Almost-Polynomial Factors is NP-Hard
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Approximating Dense Cases of Covering Problems
Approximating Dense Cases of Covering Problems
The regularity lemma and approximation schemes for dense problems
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Linear time approximation schemes for the Gale-Berlekamp game and related minimization problems
Proceedings of the forty-first annual ACM symposium on Theory of computing
Approximation schemes for the betweenness problem in tournaments and related ranking problems
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
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It is known that large fragments of the class of dense Minimum Constraint Satisfaction (MIN-CSP) problems do not have polynomial time approximation schemes (PTASs) contrary to their Maximum Constraint Satisfaction analogs. In this paper we prove, somewhat surprisingly, that the minimum satisfaction of dense instances of kSAT-formulas, and linear equations mod 2, Ek-LIN2, do have PTASs for any k. The MIN-Ek-LIN2 problems are equivalent to the k-ary versions of the Nearest Codeword problem, the problem which is known to be exceedingly hard to approximate on general instances. The method of solution of the above problems depends on the development of a new density sampling technique for k-uniform hypergraphs which could be of independent interest.