Class Description

FPR: Fixed-Parameter Randomized

Has the same relation to FPT as RP does to P.

Defined in [AR01], where it was shown that, if the Resolution proof system is automatizable (that is, if a refutation can always be found in time polynomial in the length of the shortest refutation), then W[P] is contained in FPR.

Linked From

FPT: Fixed-Parameter Tractable

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].

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