Near optimal dual fault tolerant distance oracle

We present a dual fault-tolerant distance oracle for undirected and unweighted graphs. Given a set F of two edges, as well as a source node s and a destination node t, our oracle returns the length of the shortest path from s to t that avoids F in O(1) time with a high probability. The space complexity of our oracle is $\Tilde{O}(n^2)$ \footnote{$\Tilde{O}$ hides polylogn factor }, making it nearly optimal in terms of both space and query time. Prior to our work, Pettie and Duan [SODA 2009] designed a dual fault-tolerant distance oracle that required $\Tilde{O}(n^2)$ space and O(logn) query time. In addition to improving the query time, our oracle is much simpler than the previous approach.