<s>
The	O
Karloff	B-Algorithm
–	I-Algorithm
Zwick	I-Algorithm
algorithm	I-Algorithm
,	O
in	O
computational	O
complexity	O
theory	O
,	O
is	O
a	O
randomised	B-General_Concept
approximation	B-Algorithm
algorithm	I-Algorithm
taking	O
an	O
instance	O
of	O
MAX-3SAT	B-Application
Boolean	B-Algorithm
satisfiability	I-Algorithm
problem	I-Algorithm
as	O
input	O
.	O
</s>
<s>
There	O
is	O
strong	O
evidence	O
(	O
but	O
not	O
a	O
mathematical	O
proof	O
)	O
that	O
the	O
algorithm	O
achieves	O
7/8	O
of	O
optimal	O
even	O
on	O
unsatisfiable	O
MAX-3SAT	B-Application
instances	O
.	O
</s>
<s>
For	O
the	O
related	O
MAX-E3SAT	O
problem	O
,	O
in	O
which	O
all	O
clauses	O
in	O
the	O
input	O
3SAT	O
formula	O
are	O
guaranteed	O
to	O
have	O
exactly	O
three	O
literals	O
,	O
the	O
simple	O
randomized	B-General_Concept
approximation	B-Algorithm
algorithm	I-Algorithm
which	O
assigns	O
a	O
truth	O
value	O
to	O
each	O
variable	O
independently	O
and	O
uniformly	O
at	O
random	O
satisfies	O
7/8	O
of	O
all	O
clauses	O
in	O
expectation	O
,	O
irrespective	O
of	O
whether	O
the	O
original	O
formula	O
is	O
satisfiable	O
.	O
</s>
<s>
The	O
Karloff	B-Algorithm
–	I-Algorithm
Zwick	I-Algorithm
algorithm	I-Algorithm
,	O
however	O
,	O
does	O
not	O
require	O
the	O
restriction	O
that	O
the	O
input	O
formula	O
should	O
have	O
three	O
literals	O
in	O
every	O
clause	O
.	O
</s>
<s>
Both	O
the	O
Karloff	B-Algorithm
–	I-Algorithm
Zwick	I-Algorithm
algorithm	I-Algorithm
and	O
the	O
above	O
simple	O
algorithm	O
are	O
therefore	O
optimal	O
in	O
this	O
sense	O
.	O
</s>
