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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, ⍀ n log n… (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)

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

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)

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

- Volker Priebe
- 2001

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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