Average update times for fully-dynamic all-pairs shortest paths Original Research Article

We study the fully-dynamic all pairs shortest path problem for graphs with arbitrary non-negative edge weights. It is known for digraphs that an update of the distance matrix costs image worst-case time (Thorup, 2005 ) and image amortized time (Demetrescu and Italiano, 2004 ) where image is the number of vertices. We present the first average-case analysis of the undirected problem. For a random update we show that the expected time per update is bounded by image for all image. If the graph is outside the critical window, we prove even smaller bounds.