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
Approximability of Dense Instances of NEAREST CODEWORD Problem
Approximability of Dense Instances of NEAREST CODEWORD Problem
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Approximability of Dense Instances of NEAREST CODEWORD Problem
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Approximation Hardness of Bounded Degree MIN-CSP and MIN-BISECTION
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Polynomial time approximation schemes for dense instances of minimum constraint satisfaction
Random Structures & Algorithms
ACM Transactions on Algorithms (TALG)
Limits on the Hardness of Lattice Problems in lp Norms
Computational Complexity
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
Deterministic Approximation Algorithms for the Nearest Codeword Problem
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
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We consider the following optimization problem: given a system of m linear equations in n variables over a certain field, a feasible solution is any assignment of values to the variables, and the minimized objective function is the number of equations that are not satisfied. For the case of the finite field GF[2], this problem is also known as the Nearest Codeword problem. In this note we show that for any constant c there exists a randomized polynomial time algorithm that approximates the above problem, called the Minimum Unsatisfiability of Linear Equations (MIN-UNSATISFY for short), with n/(c log n) approximation ratio. Our results hold for any field in which systems of linear equations can be solved in polynomial time.