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 shortest path from s to t avoiding F in O((cf log(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).