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A deterministic $(2 + \varepsilon)$-approximation for directed feedback vertex sets in tournaments
We nearly settle the polynomial-time approximability of the Directed Feedback Vertex Set problem in tournaments. This problem is Vertex Cover-hard, and thus cannot have a $(2 - \varepsilon)$-approximation for any $\varepsilon > 0$ in polynomial time assuming the Unique Games Conjecture. In the past
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