Completely inapproximable monotone and antimonotone parameterized problems

11/10/2017

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by   Dániel Marx, et al.

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We prove that weighted circuit satisfiability for monotone or antimonotone circuits has no fixed-parameter tractable approximation algorithm with any approximation ratio function ρ, unless FPT≠ W[1]. In particular, not having such an fpt-approximation algorithm implies that these problems have no polynomial-time approximation algorithms with ratio ρ(OPT) for any nontrivial function ρ.