Max flows in O(nm) time, or better
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 u...
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| Format: | Article |
| Language: | en_US |
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Association for Computing Machinery
2014
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| Online Access: | http://hdl.handle.net/1721.1/88020 https://orcid.org/0000-0002-7488-094X |
| Summary: | 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). |
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