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Unformatted text preview: arXiv:0809.1379v2 [cs.IT] 30 Jan 2009 1 A Max-Flow Min-Cut Theorem with Applications in Small Worlds and Dual Radio Networks Rui A. Costa Joao Barros Abstract Intrigued by the capacity of random networks, we start by proving a max-flow min-cut theorem that is applicable to any random graph obeying a suitably defined independence-in-cut property. We then show that this property is satisfied by relevant classes, including small world topologies, which are pervasive in both man-made and natural networks, and wireless networks of dual devices, which exploit multiple radio interfaces to enhance the connectivity of the network. In both cases, we are able to apply our theorem and derive max-flow min-cut bounds for network information flow. Index Terms random graphs, capacity, small world networks, wireless networks I. INTRODUCTION In the quest for the fundamental limits of communication networks, whose topology is typically described by graphs, the connection between the maximum information flow and the minimum cut of the network plays a singular and prominent role. In the case where the network has one or more independent sources of information but only one sink, it is known that the transmitted information behaves like water in pipes and the capacity can be obtained by classical network Rui A. Costa is with the Instituto de Telecomunicac oes and the Departamento de Ciencia dos Computadores da Faculdade de Ciencias da Universidade do Porto, Porto, Portugal; URL: http://www.dcc.fc.up.pt/ ruicosta/ . Joao Barros is with the Instituto de Telecomunicac oes and the Departamento de Engenharia Electrotecnica e de Computadores da Faculdade de Engenharia da Universidade do Porto, Porto, Portugal; URL: http://paginas.fe.up.pt/ jbarros/ . This work was supported by the Fundac ao para a Ciencia e Tecnologia (Portuguese Foundation for Science and Technology) under grants SFRH-BD-27273-2006 and POSC/EIA/62199/2004. Parts of this work have been presented at ITW 2006 , NetCod 2006 , and SpaSWiN 2007 . January 30, 2009 DRAFT flow methods. Specifically, the capacity of this network will then follow from the well-known Ford-Fulkerson max-flow min-cut theorem , which asserts that the maximal amount of a flow (provided by the network) is equal to the capacity of a minimal cut, i.e. a nontrivial partition of the graph node set V into two parts such that the sum of the capacities of the edges connecting the two parts (the cut capacity) is minimum. Provided there is only a single sink, routing offers an optimal solution for transporting messages both when they are statistically independent  and when they are generated by correlated sources ....
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This note was uploaded on 11/09/2010 for the course ORIE 4350 taught by Professor Shmoys during the Fall '08 term at Cornell University (Engineering School).
- Fall '08