# Path Finding II : An Õ(m sqrt(n)) Algorithm for the Minimum Cost Flow Problem

@article{Lee2013PathFI, title={Path Finding II : An {\~O}(m sqrt(n)) Algorithm for the Minimum Cost Flow Problem}, author={Y. Lee and Aaron Sidford}, journal={arXiv: Data Structures and Algorithms}, year={2013} }

In this paper we present an $\tilde{O}(m\sqrt{n}\log^{O(1)}U)$ time algorithm for solving the maximum flow problem on directed graphs with $m$ edges, $n$ vertices, and capacity ratio $U$. This improves upon the previous fastest running time of $O(m\min\left(n^{2/3},m^{1/2}\right)\log\left(n^{2}/m\right)\log U)$ achieved over 15 years ago by Goldberg and Rao. In the special case of solving dense directed unit capacity graphs our algorithm improves upon the previous fastest running times of of $O… CONTINUE READING

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