  A feedback vertex set (FVS) in a digraph is a subset of vertices whose
removal makes the digraph acyclic. In other words, it hits all cycles in the
digraph. Lokshtanov et al. [TALG '21] gave a factor 2 randomized approximation
algorithm for finding a minimum weight FVS in tournaments. We generalize the
result by presenting a factor $2\alpha$ randomized approximation algorithm for
finding a minimum weight FVS in digraphs of independence number $\alpha$; a
generalization of tournaments which are digraphs with independence number $1$.
Using the same framework, we present a factor $2$ randomized approximation
algorithm for finding a minimum weight Subset FVS in tournaments: given a
vertex subset $S$ in addition to the graph, find a subset of vertices that hits
all cycles containing at least one vertex in $S$. Note that FVS in tournaments
is a special case of Subset FVS in tournaments in which $S = V(T)$.
