Consider the minimal weights of paths between two points in a complete graph Kn with random weights on the edges, the weights being, for instance, uniformly distributed. It is shown that, asymptotically, this is log n/n for two given points, that the maximum if one point is fixed and the other varies is 2 log n/n, and that the maximum over all pairs of points is 3 log n/n.
Some further related results are given as well, including results on asymptotic distributions and moments, and on the number of edges in the minimal weight paths.
Email your librarian or administrator to recommend adding this journal to your organisation's collection.
* Views captured on Cambridge Core between September 2016 - 25th May 2017. This data will be updated every 24 hours.