Problem
Old Time
New Time
Approx.
s-t
min-cut
O
*
(
mn
)
O
*
(
n
2
/
e
2
)
Approx.
s-t
max-flow
O
*
(
m
3/2
)
O
*
(
mn
1/2
/
e
)
Flow of value
v
O
*
(
mv
)
O
*
(
n
11/9
v
)
Approx. bisection
O
*
(
m
2
)
O
*
(
n
2
/
e
2
)
m
Þ
n
/
e
2
in weighted, undirected graphs