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

Authors:
Mikkel Thorup
Affiliations:
AT&T Labs---Research, Shannon Laboratory, Florham Park, NJ
Venue:
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Year:
2005

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Abstract

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.