An Almost-Linear-Time Algorithm for Approximate Max Flow in Undirected Graphs, and its Multicommodity Generalizations

@inproceedings{Kelner2014AnAA,
  title={An Almost-Linear-Time Algorithm for Approximate Max Flow in Undirected Graphs, and its Multicommodity Generalizations},
  author={Jonathan A. Kelner and Lorenzo Orecchia and Yin Tat Lee and Aaron Sidford},
  booktitle={SODA},
  year={2014}
}
In this paper, we introduce a new framework for approximately solving flow problems in capacitated, undirected graphs and apply it to provide asymptotically faster algorithms for the maximum s-t flow and maximum concurrent multicommodity flow problems. For graphs with n vertices and m edges, it allows us to find an e-approximate maximum s-t flow in time O(m1+o(1)e-2), improving on the previous best bound of O(mn1/3poly(e-1)). Applying the same framework in the multicommodity setting solves a… 
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