Fixed-Parameter and Approximation Algorithms: A New Look

@article{Chitnis2013FixedParameterAA,
  title={Fixed-Parameter and Approximation Algorithms: A New Look},
  author={Rajesh Hemant Chitnis and Mohammad Taghi Hajiaghayi and Guy Kortsarz},
  journal={ArXiv},
  year={2013},
  volume={abs/1308.3520}
}
A Fixed-Parameter Tractable (FPT) ρ-approximation algorithm for a minimization (resp. maximization) parameterized problem P is an FPT algorithm that, given an instance (x, k) ∈ P computes a solution of cost at most k ·ρ(k) (resp. k/ρ(k)) if a solution of cost at most (resp. at least) k exists; otherwise the output can be arbitrary. For well-known intractable problems such as the W[1]-hard Clique and W[2]-hard Set Cover problems, the natural question is whether we can get any FPT-approximation… 
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