<s>
In	O
constraint	B-Application
satisfaction	I-Application
,	O
local	B-Application
search	I-Application
is	O
an	O
incomplete	O
method	O
for	O
finding	O
a	O
solution	O
to	O
a	O
problem	B-Application
.	O
</s>
<s>
In	O
particular	O
,	O
local	B-Application
search	I-Application
algorithms	O
typically	O
modify	O
the	O
value	O
of	O
a	O
variable	O
in	O
an	O
assignment	O
at	O
each	O
step	O
.	O
</s>
<s>
The	O
new	O
assignment	O
is	O
close	O
to	O
the	O
previous	O
one	O
in	O
the	O
space	O
of	O
assignment	O
,	O
hence	O
the	O
name	O
local	B-Application
search	I-Application
.	O
</s>
<s>
All	O
local	B-Application
search	I-Application
algorithms	O
use	O
a	O
function	O
that	O
evaluates	O
the	O
quality	O
of	O
assignment	O
,	O
for	O
example	O
the	O
number	O
of	O
constraints	O
violated	O
by	O
the	O
assignment	O
.	O
</s>
<s>
The	O
aim	O
of	O
local	B-Application
search	I-Application
is	O
that	O
of	O
finding	O
an	O
assignment	O
of	O
minimal	O
cost	O
,	O
which	O
is	O
a	O
solution	O
if	O
any	O
exists	O
.	O
</s>
<s>
Two	O
classes	O
of	O
local	B-Application
search	I-Application
algorithms	O
exist	O
.	O
</s>
<s>
The	O
first	O
one	O
is	O
that	O
of	O
greedy	B-Algorithm
or	O
non-randomized	O
algorithms	O
.	O
</s>
<s>
The	O
main	O
problem	B-Application
of	O
these	O
algorithms	O
is	O
the	O
possible	O
presence	O
of	O
plateaus	O
,	O
which	O
are	O
regions	O
of	O
the	O
space	O
of	O
assignments	O
where	O
no	O
local	O
move	O
decreases	O
cost	O
.	O
</s>
<s>
The	O
second	O
class	O
of	O
local	B-Application
search	I-Application
algorithm	O
have	O
been	O
invented	O
to	O
solve	O
this	O
problem	B-Application
.	O
</s>
<s>
They	O
escape	O
these	O
plateaus	O
by	O
doing	O
random	O
moves	O
,	O
and	O
are	O
called	O
randomized	O
local	B-Application
search	I-Application
algorithms	O
.	O
</s>
<s>
The	O
most	O
basic	O
form	O
of	O
local	B-Application
search	I-Application
is	O
based	O
on	O
choosing	O
the	O
change	O
that	O
maximally	O
decreases	O
the	O
cost	O
of	O
the	O
solution	O
.	O
</s>
<s>
GSAT	B-Application
(	O
greedy	B-Algorithm
sat	O
)	O
was	O
the	O
first	O
local	B-Application
search	I-Application
algorithm	O
for	O
satisfiability	O
,	O
and	O
is	O
a	O
form	O
of	O
hill	O
climbing	O
.	O
</s>
<s>
Tabu	O
search	O
overcomes	O
this	O
problem	B-Application
by	O
maintaining	O
a	O
list	O
of	O
"	O
forbidden	O
"	O
assignments	O
,	O
called	O
the	O
tabu	O
list	O
.	O
</s>
<s>
A	O
random	O
walk	O
algorithm	O
sometimes	O
moves	O
like	O
a	O
greedy	B-Algorithm
algorithm	I-Algorithm
but	O
sometimes	O
moves	O
randomly	O
.	O
</s>
<s>
At	O
every	O
move	O
,	O
with	O
probability	O
the	O
algorithm	O
proceeds	O
like	O
a	O
greedy	B-Algorithm
algorithm	I-Algorithm
,	O
trying	O
to	O
maximally	O
decrease	O
the	O
cost	O
of	O
the	O
assignment	O
.	O
</s>
<s>
The	O
random	O
move	O
of	O
WalkSAT	B-Application
is	O
changing	O
the	O
value	O
of	O
a	O
random	O
variable	O
of	O
a	O
random	O
violated	O
constraint	O
.	O
</s>
<s>
For	O
propositional	B-Algorithm
satisfiability	I-Algorithm
of	O
conjunctive	B-Application
normal	I-Application
form	I-Application
formulae	O
,	O
which	O
is	O
the	O
original	O
settings	O
of	O
this	O
algorithm	O
,	O
every	O
such	O
a	O
move	O
changes	O
the	O
value	O
of	O
the	O
variable	O
from	O
true	O
to	O
false	O
or	O
vice	O
versa	O
,	O
and	O
produce	O
the	O
satisfiability	O
of	O
the	O
violated	O
constraint	O
.	O
</s>
<s>
Local	B-Application
search	I-Application
usually	O
works	O
on	O
all	O
variables	O
,	O
improving	O
a	O
complete	O
assignment	O
to	O
them	O
.	O
</s>
<s>
However	O
,	O
local	B-Application
search	I-Application
can	O
also	O
be	O
run	O
on	O
a	O
subset	O
of	O
variables	O
,	O
using	O
some	O
other	O
mechanism	O
for	O
the	O
other	O
variables	O
.	O
</s>
<s>
A	O
proposed	O
algorithm	O
works	O
on	O
a	O
cycle	O
cutset	O
,	O
which	O
is	O
a	O
set	O
of	O
variables	O
that	O
,	O
if	O
removed	O
from	O
the	O
problem	B-Application
,	O
makes	O
it	O
acyclic	O
.	O
</s>
<s>
For	O
any	O
assignment	O
of	O
the	O
variables	O
of	O
the	O
cutset	O
,	O
the	O
remaining	O
problem	B-Application
has	O
a	O
forest	O
as	O
primal	O
graph	O
.	O
</s>
<s>
In	O
order	O
to	O
guide	O
local	B-Application
search	I-Application
,	O
an	O
algorithm	O
detecting	O
the	O
minimal	O
number	O
of	O
constraints	O
that	O
can	O
be	O
violated	O
is	O
used	O
in	O
place	O
of	O
a	O
satisfiability	O
algorithm	O
on	O
the	O
for	O
forest	O
part	O
of	O
the	O
problem	B-Application
.	O
</s>
<s>
The	O
cost	O
of	O
variable	O
evaluations	O
can	O
be	O
used	O
by	O
local	B-Application
search	I-Application
for	O
computing	O
the	O
cost	O
of	O
a	O
solution	O
.	O
</s>
