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Optimal Multicommodity Flow Through the Complete Graph with Random Edge Capacities

Part of: Graph theory

Published online by Cambridge University Press:  14 July 2016

Mustafa Khandwawala  and
Rajesh Sundaresan
Mustafa Khandwawala*
Affiliation:
Indian Institute of Science
Rajesh Sundaresan*
Affiliation:
Indian Institute of Science
*
∗ Postal address: Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore 560012, India.
∗ Postal address: Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore 560012, India.
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Abstract

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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.

Keywords

Complete graphfairnessmulticommodity flowrouteingutility

MSC classification

Secondary: 05C21: Flows in graphs 05C80: Random graphs 90C25: Convex programming

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 1 , March 2010 , pp. 201 - 215
Copyright
Copyright © Applied Probability Trust 2010 

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