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Optimal Multicommodity Flow Through the Complete Graph with Random Edge Capacities
Published online by Cambridge University Press: 14 July 2016
Abstract
We consider a multicommodity flow problem on a complete graph whose edges have random, independent, and identically distributed capacities. We show that, as the number of nodes tends to infinity, the maximum utility, given by the average of a concave function of each commodity flow, has an almost-sure limit. Furthermore, the asymptotically optimal flow uses only direct and two-hop paths, and can be obtained in a distributed manner.
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- Copyright © Applied Probability Trust 2010
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