The paper proves NP-hardness for minimum safe sets in traceable acyclic digraphs and tournaments, gives a polynomial algorithm for tournaments with small strong components, but its ETH lower bound for slightly larger components is invalid.
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Safe sets in digraphs
The paper proves NP-hardness for minimum safe sets in traceable acyclic digraphs and tournaments, gives a polynomial algorithm for tournaments with small strong components, but its ETH lower bound for slightly larger components is invalid.