Worst-case update times for fully-dynamic all-pairs shortest paths

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(<i>n</i><sup>3</sup>log ⁄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 <i>Õ</i>(<i>n</i><sup>2.75</sup>) time.

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