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�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((cflog(nW))O(f2)) time, where c>1 is a constant. The space complexity of our oracle is O(f4n2log2(nW)). For a constant f, our oracle is nearly optimal both in terms of space and time (barring some logarithmic factor).