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We review how to solve the all-pairs shortest-path problem in a nonnegatively Ž 2. weighted digraph with n vertices in expected time O n log n. This bound is shown to hold with high probability for a wide class of probability distributions on nonnegatively weighted Ž. digraphs. We also prove that, for a large class of probability distributions, ⍀ n log n(More)
We study the average-case complexity of shortest-paths problems in the vertex-potential model. The vertex-potential model is a family of probability distributions on complete directed graphs with arbitrary real edge lengths, but without negative cycles. We show that on a graph with n vertices and with respect to this model, the single-source shortest-paths(More)
We study both upper and lower bounds on the average-case complexity of shortest-paths algorithms. It is proved that the all-pairs shortest-paths problem on n-vertex networks can be solved in time O(n 2 log n) with high probability with respect to various probability distributions on the set of inputs. Our results include the first theoretical analysis of(More)
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