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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, V n log n time is necessary with high probability to compute shortest-path distances with respect to a single Ž . source. Q 1997 John Wiley & Sons, Inc. Random Struct. Alg., 10, 205]22

On the all-pairs shortest-path algorithm of Moffat and Takaoka