On the complexity of approximating the independent set problem
Information and Computation
Randomized algorithms
Computational Complexity
The hardness of approximate optima in lattices, codes, and systems of linear equations
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
On the approximability of minimizing nonzero variables or unsatisfied relations in linear systems
Theoretical Computer Science
A PCP characterization of NP with optimal amortized query complexity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Approximating maximum satisfiable subsystems of linear equations of bounded width
Information Processing Letters
On the approximability of the maximum feasible subsystem problem with 0/1-coefficients
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Hardness of Solving Sparse Overdetermined Linear Systems: A 3-Query PCP over Integers
ACM Transactions on Computation Theory (TOCT)
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Max-Satisfy is the problem of finding an assignment that satisfies the maximum number of equations in a system of linear equations over Q. We prove that unless NP ⊂ BPP Max-Satisfy cannot be efficiently approximated within an approximation ratio of 1/n1-ε, if we consider systems of n linear equations with at most n variables and ε 0 is an arbitrarily small constant. Previously, it was known that the problem is NP-hard to approximate within a ratio of 1/nα, but 0