Max flows in O(nm) time, or better
Name
Orlin_O(nm)MaxFlow.pdf
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522.52 KB
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Adobe PDF
Checksum (MD5)
8e89c2eb4709bb28b6c261c072acaba5
Author(s)
Orlin, James B
Date Issued
June 2013
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
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).
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1145/2488608.2488705
