# Routing under balance

@article{Ene2016RoutingUB, title={Routing under balance}, author={Alina Ene and Gary L. Miller and Jakub W. Pachocki and Aaron Sidford}, journal={ArXiv}, year={2016}, volume={abs/1603.09009} }

We introduce the notion of <em>balance</em> for directed graphs: a weighted directed graph is α-balanced if for every cut <i>S</i> ⊆ <i>V</i>, the total weight of edges going from <i>S</i> to <i>V</i>∖ <i>S</i> is within factor α of the total weight of edges going from <i>V</i>∖ <i>S</i> to <i>S</i>. Several important families of graphs are nearly balanced, in particular, Eulerian graphs (with α = 1) and residual graphs of (1+є)-approximate undirected maximum flows (with α=<i>O</i>(1/є)).
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