Uniform multicommodity flow through the complete graph with random edge-capacities. - Aldous, D; McDiarmid, C; Scott, A (2009)
Give random capacities C to the edges of the complete n-vertex graph. Consider the maximum flow Φ n that can be simultaneously routed between each source-destination pair. We prove that Φ n → φ{symbol} in probability where the limit constant φ{symbol} 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. © 2009 Elsevier B.V. All rights reserved.