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 $O(f^4n^2\log^2 (nW))$. For a constant $f$, our oracle is nearly optimal both in terms of space and time (barring some logarithmic factor).

翻译：我们针对边权为整数的无向加权图（边权取值范围为$[1 \dots W]$）提出了一个$f$边容错的距离查询器。给定一个包含$f$条边的故障集合$F$，以及源节点$s$和目的节点$t$，该查询器能在$O((cf \log (nW))^{O(f^2)})$时间内返回从$s$到$t$避开$F$的\emph{最短路径}，其中$c > 1$为常数。本查询器的空间复杂度为$O(f^4n^2\log^2 (nW))$。对于常数$f$，该查询器在空间和时间复杂度上均达到近乎最优（除对数因子外）。