Improved Distance Oracles for Avoiding Link-Failure

We consider the problem of preprocessing an edge-weighted directed graph to answer queries that ask for the shortest path from any given vertex to another avoiding a failed link. We present two algorithms that improve on earlier results for this problem. Our first algorithm, which is a modification of an earlier method, improves the query time to a constant while maintaining the earlier bounds for preprocessing time and space. Our second result is a new algorithm whose preprocessing time is considerably faster than earlier results and whose query time and space are worse by no more than a logarithmic factor