Completely inapproximable monotone and antimonotone parameterized problems

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]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)ρ(OPT) for any nontrivial function ρ.

► We show fpt-inapproximability results for natural problems.
► Results are under the standard complexity assumption that FPT is different from W[1]W[1].
► Weighted Monotone Circuit Satisfiability has no fpt-approximation for any ratio.
► Weighted Antimonotone Circuit Satisfiability has no fpt-approximation for any ratio.