Electrical flows, laplacian systems, and faster approximation of maximum flow in undirected graphs

@inproceedings{Christiano2011ElectricalFL,
  title={Electrical flows, laplacian systems, and faster approximation of maximum flow in undirected graphs},
  author={Paul Christiano and Jonathan A. Kelner and Aleksander Madry and Daniel A. Spielman and Shang-Hua Teng},
  booktitle={STOC '11},
  year={2011}
}
We introduce a new approach to computing an approximately maximum s-t flow in a capacitated, undirected graph. This flow is computed by solving a sequence of electrical flow problems. Each electrical flow is given by the solution of a system of linear equations in a Laplacian matrix, and thus may be approximately computed in nearly-linear time. Using this approach, we develop the fastest known algorithm for computing approximately maximum s-t flows. For a graph having n vertices and m edges… 

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