MPI-INF/SWS Research Reports 1991-2021

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An $O(n^3)$-time maximum-flow algorithm

Cheriyan, Joseph and Hagerup, Torben and Mehlhorn, Kurt

November 1991, 30 pages.

Status: available - back from printing

We show that a maximum flow in a network with $n$ vertices can be computed deterministically in $O({{n^3}/{\log n}})$ time on a uniform-cost RAM. For dense graphs, this improves the previous best bound of $O(n^3)$. The bottleneck in our algorithm is a combinatorial problem on (unweighted) graphs. The number of operations executed on flow variables is $O(n^{8/3}(\log n)^{4/3})$, in contrast with $\Omega(nm)$ flow operations for all previous algorithms, where $m$ denotes the number of edges in the network. A randomized version of our algorithm executes $O(n^{3/2}m^{1/2}\log n+n^2(\log n)^2/ \log(2+n(\log n)^2/m))$ flow operations with high probability. For the special case in which all capacities are integers bounded by $U$, we show that a maximum flow can be computed

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  AUTHOR = {Cheriyan, Joseph and Hagerup, Torben and Mehlhorn, Kurt},
  TITLE = {An $O(n^3)$-time maximum-flow algorithm},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-91-120},
  MONTH = {November},
  YEAR = {1991},
  ISSN = {0946-011X},