# A 2-Approximation Algorithm for Feedback Vertex Set in Tournaments

A tournament is a directed graph T such that every pair of vertices is connected by an arc. A feedback vertex set is a set S of vertices in T such that T - S is acyclic. We consider the Feedback Vertex Set problem in tournaments. Here the input is a tournament T and a weight function w : V(T) →N and the task is to find a feedback vertex set S in T minimizing w(S) = ∑_v ∈ S w(v). We give the first polynomial time factor 2 approximation algorithm for this problem. Assuming the Unique Games conjecture, this is the best possible approximation ratio achievable in polynomial time.

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