2-Approximating Feedback Vertex Set in Tournaments

A tournament is a directed graph T such that every pair of vertices connected by an arc. feedback vertex set S in − acyclic. We consider the Feedback Vertex Set problem tournaments. Here, input and weight function w : V ( ) → N, task to find minimizing = ∑ v∈S v ). Rounding optimal solutions natural LP-relaxation this yields simple 3-approximation algorithm. This has been improved 2.5 Cai et al. [SICOMP 2000], subsequently 7/3 Mnich [ESA 2016]. In article, we give first polynomial time factor 2-approximation algorithm for problem. Assuming Unique Games Conjecture, best possible approximation ratio achievable time.