Solving Independent Set through Vertex Cover

Question

I have an Independent Set problem, in which I have to check if given graph has a IS of given size $k$. I've already written a Vertex Cover algorithm a while back and I hope I can reuse it here. Those algorithms are closely related, since if graph $G = (V, E)$ has IS of size $k$ iff it has VC of size $V - k$. So am I right that I can I just use my VC algorithm with $k' = V - k$?

I've read this and this question and after that I've started doubting that this is that simple.

Answer 1

It is that simple, those questions are talking about fixed parameter tractable algorithms w.r.t. the size $k$ of an independent set/vertex cover. Your algorithm will work just fine setting $k' = |V| - k$. Clearly, the new value $k'$ also affects the running time of your algorithm.