Worst-case update times for fully-dynamic all-pairs shortest paths
Mikkel Thorup · 2005
We present here the first solution to the fully-dynamic all pairs shortest path problem where every update is faster than a recomputation from scratch in Ω(n3log ⁄n) time. This is for a directed graph with arbitrary non-negative edge weights. An update inserts or deletes a vertex with all incident edges. After each such vertex update, we update a complete distance matrix in Õ(n2.75) time.