# 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…

## 21 Citations

Fault-Tolerant Subgraph for Single-Source Reachability: General and Optimal

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A decremental data structure is introduced that supports sensitivity queries of the form "are u and v strongly connected in the graph G \setminus w $?", for any triple of vertices of a directed graph (digraph) under edge deletions, and answers the above queries in constant time.

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The problem of single source reachability from s in presence of failures of vertices/edges is addressed and it is shown that for every k≥ 1, there is a subgraph H of G with at most 2k n edges that preserves the reachable from s even after the failure of any k edges.

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An application of low-high orders in faulttolerant network design that is presented recently and shows that there is a valid set containing at most n − 1 arcs, and an algorithm to compute a minimum-size valid set in O(mlog n) time is given.

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This paper shows that given any weighted directed graph with $n$ vertices and a source vertex, one can construct a subgraph that contains at most $e \cdot (k-1)!2^kn$ many edges such that it preserves distances between the source and all other vertices as long as the total weight increment is bounded by $k.

Fault Tolerant Subgraphs with Applications in Kernelization

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It is proved that “almost acyclicity” suffices to eliminate the dependency on n entirely for a broad class of dense digraphs called bounded independence dig graphs, and DEOCT is proved to be NP-hard on tournaments by establishing a combinatorial identity between the minimum size of a feedback arc set and theminimum size of an edge odd cycle transversal.

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