On the all-pairs shortest-path algorithm of Moffat and Takaoka
暂无分享,去创建一个
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
[1] M. Hofri. Analysis of Algorithms: Computational Methods & Mathematical Tools , 1995 .
[2] C. E. Veni Madhavan. Foundations of Software Technology and Theoretical Computer Science , 1988, Lecture Notes in Computer Science.
[3] Alistair Moffat,et al. An all pairs shortest path algorithm with expected running time O(n 2logn) , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).
[4] W. Hoeffding. Probability Inequalities for sums of Bounded Random Variables , 1963 .