The class of optimization problems such that, given an instance of length n, we can find a solution within a factor 1+ε of the optimum in time f(ε)p(n), where p is a polynomial and f is arbitrary.
Contains FPTAS and is contained in PTAS.
Defined in [CT97], where the following was also shown:
The class of decision problems of the form (x,k), k a parameter, that are solvable in time f(k)p(|x|), where f is arbitrary and p is a polynomial.
The basic class of the theory of fixed-parameter tractability, as described by Downey and Fellows [DF99].
To separate FPT and W[2], one could show there is no proof system for CNF formulae that admits proofs of size f(k)nO(1), where f is a computable function and n is the size of the formula.
Contained in FPTnu, W[1], and FPR.
Contains FPTAS [CC97], as well as FPTsu.
Contains EPTAS unless FPT = W[1] [Baz95].