Algorithms – Execution time in FPT

No, a runtime like $ f (k) n g (n, k)} $ it is not suitable for any non-constant function $ g $.

$ mathrm {FPT} $ It is the kind of problems computable in time. $ O (f (k) cdot n ^ {c}) $ for some fixed $ c in mathbb {N} $. The "fixed" is very important, just like $ mathrm {P} $ It is the kind of problems computable in time. $ O (n ^ {c}) $ for some arranged $ c $ – you do not even have a small non-constant function (like $ n ^ { log n} $) in the exponent and still be in $ mathrm {P} $.