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

Cheriyan, Joseph and Hagerup, Torben and Mehlhorn, Kurt

MPI-I-91-120. November 1991, 30 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
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},