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- Kurt Mehlhorn, Volker Priebe
- ESA
- 1995

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… (More)

- Colin Cooper, Alan M. Frieze, Kurt Mehlhorn, Volker Priebe
- RANDOM
- 1997

We study the average-case complexity of shortest-paths problems in the vertexpotential 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 investigate random variables arising in occupancy problems, and show the variables to be negatively associated, that is, negatively dependent in a strong sense. Our proofs are based on the FKG correlation inequality, and they suggest a useful, general technique for proving negative dependence among random variables. We also show that in the special case… (More)

- Volker Priebe
- 2001

We study both upper and lower bounds on the average-case complexity of shortestpaths algorithms. It is proved that the all-pairs shortest-paths problem on n-vertex networks can be solved in time O(n2 logn) with high probability with respect to various probability distributions on the set of inputs. Our results include the first theoretical analysis of the… (More)

- Kurt Mehlhorn, Volker Priebe, Guido Schäfer, Naveen Sivadasan
- Inf. Process. Lett.
- 2002

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