I want to know whether there is a relation between parameterized algorithms and approximation algorithms.

Like there will exist a fpt problem for problem P iff it have some f-approx algorithm.

I would be also happy if some one can give me reference.

Edit: It's just observation from my aspect that c-approx algo have fpt algo where c is constant. I am not able to prove it but I want contradicting example.

Also this implies there is a relation between kernel and the approximation algo.

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    $\begingroup$ What research have you done? $\endgroup$ – Raphael Apr 5 '16 at 15:43
  • $\begingroup$ I think I have proof in one direction, I.e, fpt implies c-aprrox algo. we will find the a k kernal for problem P then use this as approx algo solution. Now we can traverse k=1 to n for optimal parameter. $\endgroup$ – Thinking Apr 6 '16 at 10:14
  • $\begingroup$ How does the size bound translate into a quality bound? $\endgroup$ – Raphael Apr 6 '16 at 11:22
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    $\begingroup$ yeah, this works for linear kernel only did not notice earliar. $\endgroup$ – Thinking Apr 6 '16 at 12:45