An Improved FPT Algorithm for Independent Feedback Vertex Set

Summary

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+ϕ2)k)- time FPT algorithm for this problem, whereϕ < 1.619 is the golden ratio, improving the previous fastest O∗ (4.1481k)-time algorithm given by Agrawal et al. (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