<s>
In	O
the	O
theory	O
of	O
combinatorial	O
optimization	O
,	O
submodular	B-Algorithm
flow	I-Algorithm
is	O
a	O
general	O
class	O
of	O
optimization	O
problems	O
that	O
includes	O
as	O
special	O
cases	O
the	O
minimum-cost	B-Algorithm
flow	I-Algorithm
problem	I-Algorithm
,	O
matroid	B-Algorithm
intersection	I-Algorithm
,	O
and	O
the	O
problem	O
of	O
computing	O
a	O
minimum-weight	O
dijoin	O
in	O
a	O
weighted	O
directed	O
graph	O
.	O
</s>
<s>
In	O
the	O
classical	O
minimum-cost	B-Algorithm
flow	I-Algorithm
problem	I-Algorithm
,	O
the	O
input	O
is	O
a	O
flow	B-Algorithm
network	I-Algorithm
,	O
with	O
given	O
capacities	O
that	O
specify	O
lower	O
and	O
upper	O
limits	O
on	O
the	O
amount	O
of	O
flow	O
per	O
edge	O
,	O
as	O
well	O
as	O
costs	O
per	O
unit	O
flow	O
along	O
each	O
edge	O
.	O
</s>
<s>
In	O
submodular	B-Algorithm
flow	I-Algorithm
,	O
as	O
well	O
,	O
one	O
is	O
given	O
a	O
submodular	B-Algorithm
set	I-Algorithm
function	I-Algorithm
on	O
sets	O
of	O
vertices	O
of	O
the	O
graph	O
.	O
</s>
<s>
Instead	O
of	O
obeying	O
Kirchhoff	O
's	O
law	O
,	O
it	O
is	O
a	O
requirement	O
that	O
,	O
for	O
every	O
vertex	O
set	O
,	O
the	O
excess	O
flow	O
(	O
the	O
function	O
mapping	O
the	O
set	O
to	O
its	O
difference	O
between	O
flow	O
in	O
and	O
flow	O
out	O
)	O
can	O
be	O
at	O
most	O
the	O
value	O
given	O
by	O
the	O
submodular	B-Algorithm
function	I-Algorithm
.	O
</s>
