Local Search is a PTAS for Feedback Vertex Set in Minor-free Graphs
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Given an undirected graph, the Feedback Vertex Set (FVS) problem asks for a minimum set of vertices that hits all the cycles of the graph. Fomin, Lokshtanov, Rauman and Saurabh gave a PTAS for the FVS problem in H-minor-free graphs. Their algorithm relies on many complicated algorithmic tools. In this work, we show that a simple local search algorithm, that tries to improve the solution by exchanging only constant number of vertices, is a PTAS for the FVS problem in H-minor-free graphs.
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