  Fixed-parameter algorithms, approximation algorithms and moderately
exponential algorithms are three major approaches to algorithms design. While
each of them being very active in its own, there is an increasing attention to
the connection between different approaches. In particular, whether Maximum
Independent Set would be better approximable once endowed with
subexponential-time or FPT-time is a central question. In this paper, we
present a strong link between the linear PCP conjecture and the
inapproximability, thus partially answering this question.
