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The Single Source Replacement Paths (SSRP) problem is as follows; Given a graph G = (V,E), a source vertex s and a shortest paths tree Ts rooted in s, output for every vertex t ∈ V and for every edge e in Ts the length of the shortest path from s to t avoiding e. We present near optimal upper bounds, by providing Õ(m √ n + n) time randomized combinatorial algorithm 1 for unweighted undirected graphs, and matching conditional lower bounds for the SSRP problem.

Near Optimal Algorithms For The Single Source Replacement Paths Problem