Nearly Optimal Fault Tolerant Distance Oracle

We present an $f$-fault tolerant distance oracle for an undirected weighted graph where each edge has an integral weight from $[1\dots W]$. Given a set $F$ of $f$ edges, as well as a source node $s$ and a destination node $t$, our oracle returns the \emph{shortest path} from $s$ to $t$ avoiding $F$ in $O((cf\log (nW){)}^{O(f^2)})$ time, where $c>1$ is a constant. The space complexity of our oracle is $O(f^4{n}^2{\log }^2(nW))$. For a constant $f$, our oracle is nearly optimal both in terms of space and time (barring some logarithmic factor).