Optimal Vertex Fault Tolerant Spanners (for fixed stretch)

  title={Optimal Vertex Fault Tolerant Spanners (for fixed stretch)},
  author={Gregory Bodwin and Michael Dinitz and Merav Parter and Virginia Vassilevska Williams},
A $k$-spanner of a graph $G$ is a sparse subgraph $H$ whose shortest path distances match those of $G$ up to a multiplicative error $k$. In this paper we study spanners that are resistant to faults. A subgraph $H \subseteq G$ is an $f$ vertex fault tolerant (VFT) $k$-spanner if $H \setminus F$ is a $k$-spanner of $G \setminus F$ for any small set $F$ of $f$ vertices that might "fail." One of the main questions in the area is: what is the minimum size of an $f$ fault tolerant $k$-spanner that… 

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