An improved FPT algorithm for Independent Feedback Vertex Set

We study the Independent Feedback Vertex Set problem - a variant of the classic Feedback Vertex Set problem where, given a graph $G$ and an integer $k$, the problem is to decide whether there exists a vertex set $S\subseteq V(G)$ such that $G\setminus S$ is a forest and $S$ is an independent set of size at most $k$. We present an $O^{\ast((1+\varphi{2}){k})$-time} FPT algorithm for this problem, where $\varphi<1.619$ is the golden ratio, improving the previous fastest $O^{\ast(4.1481{k})$-time} algorithm given by Agrawal et al [IPEC 2016]. The exponential factor in our time complexity bound matches the fastest deterministic FPT algorithm for the classic Feedback Vertex Set problem. On the technical side, the main novelty is a refined measure of an input instance in a branching process, that allows for a simpler and more concise description and analysis of the algorithm.