# Space-Efficient Fault-Tolerant Diameter Oracles

@article{Bil2021SpaceEfficientFD, title={Space-Efficient Fault-Tolerant Diameter Oracles}, author={Davide Bil{\`o} and Sarel Cohen and Tobias Friedrich and Martin Schirneck}, journal={ArXiv}, year={2021}, volume={abs/2107.03485} }

We design f-edge fault-tolerant diameter oracles (f -FDO, or simply FDO if f = 1). For a given directed or undirected and possibly edge-weighted graph G with n vertices and m edges and a positive integer f , we preprocess the graph and construct a data structure that, when queried with a set F of edges, where |F | ⩽ f , returns the diameter of G − F . An f -FDO has stretch σ ⩾ 1 if the returned value D̂ satisfies diam(G − F ) ⩽ D̂ ⩽ σ diam(G − F ). For the case of a single edge failure (f = 1…

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