Max flows in O(nm) time, or better

@inproceedings{Orlin2013MaxFI,
  title={Max flows in O(nm) time, or better},
  author={James B. Orlin},
  booktitle={STOC '13},
  year={2013}
}
  • J. Orlin
  • Published in STOC '13 1 June 2013
  • Computer Science
In this paper, we present improved polynomial time algorithms for the max flow problem defined on sparse networks with n nodes and m arcs. We show how to solve the max flow problem in O(nm + m31/16 log2 n) time. In the case that m = O(n1.06), this improves upon the best previous algorithm due to King, Rao, and Tarjan, who solved the max flow problem in O(nm logm/(n log n)n) time. This establishes that the max flow problem is solvable in O(nm) time for all values of n and m. In the case that m… 

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