Subexponential and FPT-time Inapproximability of Independent Set and   Related Problems
  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. 
Bruno Escoffier, EunJung Kim and Vangelis Th. Paschos
cs.CC cs.DS