# Relation between Parameterized complexity and Approximation Algorithms [duplicate]

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.

• What research have you done? – Raphael Apr 5 '16 at 15:43
• 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. – Thinking Apr 6 '16 at 10:14
• How does the size bound translate into a quality bound? – Raphael Apr 6 '16 at 11:22
• yeah, this works for linear kernel only did not notice earliar. – Thinking Apr 6 '16 at 12:45