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

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Frank-Wolfe Algorithms for Saddle Point Problems (2016, background): “For instance, if the LMO is max-ﬂow, it could have almost linear runtime while the corresponding projection would require cubic runtime quadratic programming (Kelner et al., 2014).”
Efficient Accelerated Coordinate Descent Methods and Faster Algorithms for Solving Linear Systems (2013, methodology): “…since a breakthrough result in 2004 by Spielman and Teng [27] showed that such systems can be solved in nearly-linear time, such systems have been used to create the fastest algorithm for a variety of problems ranging from max ﬂow [14] to sampling random spanning trees [13] and much more.”
An Almost-Linear-Time Algorithm for Approximate Max Flow in Undirected Graphs, and its Multicommodity Generalizations (2013, methodology): “However, for simplicity and completeness, in the full version [8] we provide a complete proof of this lemma.”