Fault Tolerant Reachability for Directed Graphs

@inproceedings{Baswana2015FaultTR,
  title={Fault Tolerant Reachability for Directed Graphs},
  author={Surender Baswana and Keerti Choudhary and Liam Roditty},
  booktitle={DISC},
  year={2015}
}
Let $$G=V,E$$ be an n-vertices m-edges directed graph. Let $$s\in V$$ be any designated source vertex, and let T be an arbitrary reachability tree rooted at s. We address the problem of finding a set of edges $$\mathcal{E}\subseteq E\backslash T$$ of minimum size such that on a failure of any vertex $$w\in V$$, the set of vertices reachable from s in $$T\cup \mathcal{E} \backslash \{w\}$$ is the same as the set of vertices reachable from s in $$G\backslash \{w\}$$. We obtain the following… 
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