An improved FPT algorithm for Independent Feedback Vertex Set

03/02/2018

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by   Shaohua Li, et al.

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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^2)^k)-time FPT algorithm for this problem, where φ<1.619 is the golden ratio, improving the previous fastest O^∗(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.