Max flows in O(nm) time, or better

Author(s)
Orlin, James B
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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 + m[superscript 31/16] log[superscript 2] n) time. In the case that m = O(n[superscript 1.06]), 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(n[superscript 2]/ log n).
Date issued
2013-06
URI
http://hdl.handle.net/1721.1/88020
Department
Massachusetts Institute of Technology. Operations Research Center; Sloan School of Management
Journal
Proceedings of the 45th annual ACM Symposium on theory of computing - STOC '13
Publisher
Association for Computing Machinery
Citation
Orlin, James B. “Max Flows in O(nm) Time, or Better.” Proceedings of the 45th Annual ACM Symposium on Theory of Computing - STOC ’13, June 1-4, 2013, Palo Alto, California, USA (2013). p.765-774.
Version: Original manuscript
ISBN
9781450320290
1450320295
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