<s>
This	O
partitioning	O
can	O
have	O
applications	O
in	O
VLSI	O
design	O
,	O
data-mining	B-Application
,	O
finite	B-Application
elements	I-Application
and	O
communication	O
in	O
parallel	B-Operating_System
computing	I-Operating_System
.	O
</s>
<s>
Several	O
approximation	B-Algorithm
algorithms	I-Algorithm
exist	O
with	O
an	O
approximation	O
of	O
A	O
simple	O
greedy	B-Algorithm
algorithm	I-Algorithm
that	O
achieves	O
this	O
approximation	O
factor	O
computes	O
a	O
minimum	O
cut	O
in	O
each	O
of	O
the	O
connected	O
components	O
and	O
removes	O
the	O
heaviest	O
one	O
.	O
</s>
<s>
This	O
algorithm	O
requires	O
a	O
total	O
of	O
max	B-Algorithm
flow	I-Algorithm
computations	O
.	O
</s>
<s>
Another	O
algorithm	O
achieving	O
the	O
same	O
guarantee	O
uses	O
the	O
Gomory	B-Algorithm
–	I-Algorithm
Hu	I-Algorithm
tree	I-Algorithm
representation	O
of	O
minimum	O
cuts	O
.	O
</s>
<s>
Constructing	O
the	O
GomoryHu	O
tree	O
requires	O
max	B-Algorithm
flow	I-Algorithm
computations	O
,	O
but	O
the	O
algorithm	O
requires	O
an	O
overall	O
max	B-Algorithm
flow	I-Algorithm
computations	O
.	O
</s>
<s>
Moreover	O
,	O
under	O
the	O
small	O
set	O
expansion	O
hypothesis	O
(	O
a	O
conjecture	O
closely	O
related	O
to	O
the	O
unique	O
games	O
conjecture	O
)	O
,	O
the	O
problem	O
is	O
NP-hard	O
to	O
approximate	O
to	O
within	O
factor	O
for	O
every	O
constant	O
,	O
meaning	O
that	O
the	O
aforementioned	O
approximation	B-Algorithm
algorithms	I-Algorithm
are	O
essentially	O
tight	O
for	O
large	O
.	O
</s>
<s>
More	O
recently	O
,	O
polynomial	B-Algorithm
time	I-Algorithm
approximation	I-Algorithm
schemes	I-Algorithm
(	O
PTAS	O
)	O
were	O
discovered	O
for	O
those	O
problems	O
.	O
</s>
<s>
While	O
the	O
minimum	O
-cut	O
problem	O
is	O
W[1]-hard	B-General_Concept
parameterized	B-General_Concept
by	O
,	O
a	O
parameterized	B-General_Concept
approximation	O
scheme	O
can	O
be	O
obtained	O
for	O
this	O
parameter	O
.	O
</s>
