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Multicommodity Flows and Approximation Algorithms (1994)
| Citations: | 5 - 0 self |
BibTeX
@MISC{Garg94multicommodityflows,
author = {Naveen Garg and Vijay V. Vazirani},
title = {Multicommodity Flows and Approximation Algorithms},
year = {1994}
}
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Abstract
This thesis is about multicommodity flows and their use in designing approximation algorithms for problems involving cuts in graphs. In a ground-breaking work Leighton and Rao [34] showed an approximate max-flow min-cut theorem for uniform multicommodity flow and used this to obtain an approximation algorithm for the flux of a graph. We consider the multicommodity flow problem in which the object is to maximize the sum of the flows routed and prove the following approximate max-flow min-multicut theorem min-multicut O(log k) max-flow min-multicut where k is the number of commodities. Our proof is based on a rounding technique from [34]. Further, we show that this theorem is tight. For a multicommodity flow instance with specified demands, the ratio of the maximum concurrent flow to the sparsest cut was shown to be bounded by O(log 2 k) [30, 57, 17, 47]. We use ideas from our proof of the approximate max-flow min-multicut theorem and a geometric scaling technique from [1] to provi...
Keyphrases
approximation algorithm multicommodity flow max-flow min-multicut multicommodity flow instance maximum concurrent flow specified demand geometric scaling technique rounding technique approximate max-flow min-cut theorem multicommodity flow problem uniform multicommodity flow ground-breaking work leighton approximate max-flow min-multicut theorem
