Max flows in O(nm) time, or better

Authors:
James B. Orlin
Affiliations:
M.I.T., Cambridge, MA, USA
Venue:
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Year:
2013

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Abstract

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 = O(n), we improve the running time to O(n2/ log n).