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Fixed-parameter algorithms, approximation algorithms and moderatelyexponential algorithms are three major approaches to algorithms design. Whileeach of them being very active in its own, there is an increasing attention tothe connection between different approaches. In particular, whether MaximumIndependent Set would be better approximable once endowed withsubexponential-time or FPT-time is a central question. In this paper, wepresent a strong link between the linear PCP conjecture and theinapproximability, thus partially answering this question.

Subexponential and FPT-time Inapproximability of Independent Set and Related Problems