From gap-exponential time hypothesis to fixed parameter tractable inapproximability: Clique, dominating set, and more

We consider questions that arise from the intersection between the areas of polynomial-time approximation algorithms, subexponential-time algorithms, and fixed-parameter tractable algorithms. Answering a long-standing open question, we show that, under standard conjectures, there is no FTP approximation algorithm for the maximum clique problem and the minimum dominating set problem