<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
iterative	B-Algorithm
compression	I-Algorithm
is	O
an	O
algorithmic	O
technique	O
for	O
the	O
design	O
of	O
fixed-parameter	B-General_Concept
tractable	I-General_Concept
algorithms	I-General_Concept
,	O
in	O
which	O
one	O
element	O
(	O
such	O
as	O
a	O
vertex	O
of	O
a	O
graph	O
)	O
is	O
added	O
to	O
the	O
problem	O
in	O
each	O
step	O
,	O
and	O
a	O
small	O
solution	O
for	O
the	O
problem	O
prior	O
to	O
the	O
addition	O
is	O
used	O
to	O
help	O
find	O
a	O
small	O
solution	O
to	O
the	O
problem	O
after	O
the	O
step	O
.	O
</s>
<s>
Odd	O
cycle	O
transversal	O
is	O
the	O
problem	O
of	O
finding	O
the	O
smallest	O
set	O
of	O
vertices	O
of	O
a	O
graph	O
that	O
include	O
at	O
least	O
one	O
vertex	O
from	O
every	O
odd	O
cycle	O
;	O
its	O
parameterized	B-General_Concept
complexity	I-General_Concept
was	O
a	O
longstanding	O
open	O
question	O
.	O
</s>
<s>
It	O
is	O
now	O
considered	O
to	O
be	O
one	O
of	O
the	O
fundamental	O
techniques	O
in	O
the	O
area	O
of	O
parameterized	B-General_Concept
algorithmics	O
.	O
</s>
<s>
Iterative	B-Algorithm
compression	I-Algorithm
has	O
been	O
used	O
successfully	O
in	O
many	O
problems	O
,	O
for	O
instance	O
odd	O
cycle	O
transversal	O
(	O
see	O
below	O
)	O
and	O
edge	O
bipartization	O
,	O
feedback	O
vertex	O
set	O
,	O
cluster	O
vertex	O
deletion	O
and	O
directed	O
feedback	O
vertex	O
set	O
.	O
</s>
<s>
Iterative	B-Algorithm
compression	I-Algorithm
applies	O
,	O
for	O
instance	O
,	O
to	O
parameterized	B-General_Concept
graph	O
problems	O
whose	O
inputs	O
are	O
a	O
graph	O
and	O
a	O
natural	O
number	O
,	O
and	O
where	O
the	O
problem	O
is	O
to	O
test	O
the	O
existence	O
of	O
a	O
solution	O
(	O
a	O
set	O
of	O
vertices	O
)	O
of	O
size	O
.	O
</s>
<s>
Therefore	O
,	O
if	O
the	O
compression	O
variant	O
is	O
solvable	O
in	O
fixed-parameter	O
tractable	O
time	O
,	O
i.e.	O
,	O
f(k )	O
·nc	O
for	O
some	O
constant	O
c	O
,	O
then	O
the	O
iterative	B-Algorithm
compression	I-Algorithm
procedure	O
solving	O
the	O
entire	O
problem	O
runs	O
in	O
f(k )	O
·nc+1	O
time	O
.	O
</s>
<s>
When	O
the	O
value	O
of	O
the	O
parameter	O
is	O
unknown	O
,	O
it	O
can	O
be	O
found	O
by	O
using	O
an	O
outer	O
level	O
of	O
exponential	B-Algorithm
search	I-Algorithm
or	O
sequential	B-Algorithm
search	I-Algorithm
for	O
the	O
optimal	O
choice	O
of	O
,	O
with	O
each	O
step	O
of	O
the	O
search	O
based	O
on	O
the	O
same	O
iterative	B-Algorithm
compression	I-Algorithm
algorithm	O
.	O
</s>
<s>
Later	O
,	O
a	O
simpler	O
algorithm	O
was	O
given	O
,	O
also	O
using	O
iterative	B-Algorithm
compression	I-Algorithm
,	O
by	O
Lokshstanov	O
,	O
Saurabh	O
and	O
Sikdar	O
.	O
</s>
<s>
Once	O
these	O
three	O
sets	O
have	O
been	O
selected	O
,	O
the	O
remaining	O
vertices	O
of	O
a	O
deletion	O
set	O
(	O
if	O
it	O
exists	O
)	O
can	O
be	O
found	O
from	O
them	O
by	O
applying	O
a	O
max-flow	B-Algorithm
min-cut	I-Algorithm
algorithm	O
.	O
</s>
<s>
Vertex	O
cover	O
is	O
another	O
example	O
for	O
which	O
iterative	B-Algorithm
compression	I-Algorithm
can	O
be	O
employed	O
.	O
</s>
<s>
Using	O
this	O
subroutine	O
in	O
an	O
iterative	B-Algorithm
compression	I-Algorithm
algorithm	O
gives	O
a	O
simple	O
algorithm	O
for	O
vertex	O
cover	O
.	O
</s>
