Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Linear FPT reductions and computational lower bounds
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
On miniaturized problems in parameterized complexity theory
Theoretical Computer Science - Parameterized and exact computation
The complexity of homomorphism and constraint satisfaction problems seen from the other side
Journal of the ACM (JACM)
On parameterized approximability
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
The birth and early years of parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
Parameterized Complexity and Approximation Algorithms
The Computer Journal
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In parameterized complexity there are three natural definitions of fixed-parameter tractability called strongly uniform, weakly uniform and nonuniform fpt. Similarly, there are three notions of subexponential time, yielding three flavours of the exponential time hypothesis (ETH) stating that 3Sat is not solvable in subexponential time. It is known that ETH implies that p-Clique is not fixed-parameter tractable if both are taken to be strongly uniform or both are taken to be uniform, and we extend this to the nonuniform case. We also show that even the containment of weakly uniform subexponential time in nonuniform subexponential time is strict. Furthermore, we deduce from nonuniform ETH that no single exponent d allows for arbitrarily good fpt-approximations of clique.