Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Give random capacities C to the edges of the complete n-vertex graph. Consider the maximum flow @F"n that can be simultaneously routed beten each source-destination pair.  prove that @F"n->@f in probability where the limit constant @f depends on the distribution of C in a simple way, and that asymptotically one need use only 1- and 2-step routes. The proof uses a reduction to a random graph problem.
['David J. Aldous', 'Colin McDiarmid', 'Alex Scott']
I am writing a research paper on a idea Uniform multicommodity flow through the complete graph with random edge-capacities
[{"from": "human", "value": "I am writing a research paper on a idea Uniform multicommodity flow through the complete graph with random edge-capacities"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Give random capacities C to the edges of the complete n-vertex graph. Consider the maximum flow @F\"n that can be simultaneously routed beten each source-destination pair.  prove that @F\"n->@f in probability where the limit constant @f depends on the distribution of C in a simple way, and that asymptotically one need use only 1- and 2-step routes. The proof uses a reduction to a random graph problem."}]