<s>
In	O
mathematical	O
optimization	O
,	O
the	O
network	B-Algorithm
simplex	I-Algorithm
algorithm	I-Algorithm
is	O
a	O
graph	O
theoretic	O
specialization	O
of	O
the	O
simplex	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
The	O
algorithm	O
is	O
usually	O
formulated	O
in	O
terms	O
of	O
a	O
minimum-cost	B-Algorithm
flow	I-Algorithm
problem	I-Algorithm
.	O
</s>
<s>
The	O
network	B-Algorithm
simplex	I-Algorithm
method	I-Algorithm
works	O
very	O
well	O
in	O
practice	O
,	O
typically	O
200	O
to	O
300	O
times	O
faster	O
than	O
the	O
simplex	B-Algorithm
method	I-Algorithm
applied	O
to	O
general	O
linear	O
program	O
of	O
same	O
dimensions	O
.	O
</s>
<s>
For	O
a	O
long	O
time	O
,	O
the	O
existence	O
of	O
a	O
provably	O
efficient	O
network	B-Algorithm
simplex	I-Algorithm
algorithm	I-Algorithm
was	O
one	O
of	O
the	O
major	O
open	O
problems	O
in	O
complexity	O
theory	O
,	O
even	O
though	O
efficient-in-practice	O
versions	O
were	O
available	O
.	O
</s>
<s>
Later	O
Tarjan	O
improved	O
this	O
to	O
using	O
dynamic	B-Data_Structure
trees	I-Data_Structure
in	O
1997	O
.	O
</s>
<s>
Strongly	O
polynomial	O
dual	O
network	B-Algorithm
simplex	I-Algorithm
algorithms	I-Algorithm
for	O
the	O
same	O
problem	O
,	O
but	O
with	O
a	O
higher	O
dependence	O
on	O
the	O
numbers	O
of	O
edges	O
and	O
vertices	O
in	O
the	O
graph	O
,	O
have	O
been	O
known	O
for	O
longer	O
.	O
</s>
<s>
The	O
network	B-Algorithm
simplex	I-Algorithm
method	I-Algorithm
is	O
an	O
adaptation	O
of	O
the	O
bounded	O
variable	O
primal	O
simplex	O
algorithm	O
.	O
</s>
<s>
The	O
network	B-Algorithm
simplex	I-Algorithm
algorithm	I-Algorithm
can	O
be	O
used	O
to	O
solve	O
many	O
practical	O
problems	O
including	O
,	O
</s>
