FPT-approximation for FPT problems

Over the past decade, many results have focused on the design of parameterized approximation algorithms for W[1]-hard problems. However, there are fundamental problems within the class FPT for which the best known algorithms have seen no progress over the course of the decade. In this paper, we expand the study of FPT-approximation and initiate a systematic study of FPT-approximation for problems that are in FPT. We design FPT-approximation algorithms for problems that are in FPT, with running times that are significantly faster than the corresponding best known FPT-algorithm, and while achieving approximation ratios that are significantly better than what is possible in polynomial time