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 ⊆ V (G) such that G \ S is a forest and S is an independent set of size at most k. We present an O∗((1 +φ))-time FPT algorithm for this problem, where φ < 1.619 is the golden ratio, improving the previous fastest O∗(4.1481k)-time algorithm given by Agrawal et al. [1]. 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.