<s>
In	O
combinatorial	O
optimization	O
,	O
network	B-Algorithm
flow	I-Algorithm
problems	I-Algorithm
are	O
a	O
class	O
of	O
computational	O
problems	O
in	O
which	O
the	O
input	O
is	O
a	O
flow	B-Algorithm
network	I-Algorithm
(	O
a	O
graph	O
with	O
numerical	O
capacities	O
on	O
its	O
edges	O
)	O
,	O
and	O
the	O
goal	O
is	O
to	O
construct	O
a	O
flow	O
,	O
numerical	O
values	O
on	O
each	O
edge	O
that	O
respect	O
the	O
capacity	O
constraints	O
and	O
that	O
have	O
incoming	O
flow	O
equal	O
to	O
outgoing	O
flow	O
at	O
all	O
vertices	O
except	O
for	O
certain	O
designated	O
terminals	O
.	O
</s>
<s>
Specific	O
types	O
of	O
network	B-Algorithm
flow	I-Algorithm
problems	I-Algorithm
include	O
:	O
</s>
<s>
The	O
max-flow	B-Algorithm
min-cut	I-Algorithm
theorem	I-Algorithm
equates	O
the	O
value	O
of	O
a	O
maximum	B-Algorithm
flow	I-Algorithm
to	O
the	O
value	O
of	O
a	O
minimum	O
cut	O
,	O
a	O
partition	O
of	O
the	O
vertices	O
of	O
the	O
flow	B-Algorithm
network	I-Algorithm
that	O
minimizes	O
the	O
total	O
capacity	O
of	O
edges	O
crossing	O
from	O
one	O
side	O
of	O
the	O
partition	O
to	O
the	O
other	O
.	O
</s>
<s>
Approximate	B-Algorithm
max-flow	I-Algorithm
min-cut	I-Algorithm
theorems	I-Algorithm
provide	O
an	O
extension	O
of	O
this	O
result	O
to	O
multi-commodity	B-Algorithm
flow	I-Algorithm
problems	I-Algorithm
.	O
</s>
<s>
The	O
Gomory	B-Algorithm
–	I-Algorithm
Hu	I-Algorithm
tree	I-Algorithm
of	O
an	O
undirected	O
flow	B-Algorithm
network	I-Algorithm
provides	O
a	O
concise	O
representation	O
of	O
all	O
minimum	O
cuts	O
between	O
different	O
pairs	O
of	O
terminal	O
vertices	O
.	O
</s>
<s>
Otherwise	O
the	O
problem	O
can	O
be	O
formulated	O
as	O
a	O
more	O
conventional	O
linear	B-Algorithm
program	I-Algorithm
or	O
similar	O
and	O
solved	O
using	O
a	O
general	O
purpose	O
optimization	O
solver	O
.	O
</s>
