<s>
In	O
mathematics	O
and	O
theoretical	O
computer	O
science	O
,	O
entropy	B-General_Concept
compression	I-General_Concept
is	O
an	O
information	O
theoretic	O
method	O
for	O
proving	O
that	O
a	O
random	O
process	O
terminates	O
,	O
originally	O
used	O
by	O
Robin	O
Moser	O
to	O
prove	O
an	O
algorithmic	O
version	O
of	O
the	O
Lovász	O
local	O
lemma	O
.	O
</s>
<s>
An	O
example	O
given	O
by	O
both	O
Fortnow	O
and	O
Tao	O
concerns	O
the	O
Boolean	B-Algorithm
satisfiability	I-Algorithm
problem	I-Algorithm
for	O
Boolean	O
formulas	O
in	O
conjunctive	B-Application
normal	I-Application
form	I-Application
,	O
with	O
uniform	O
clause	O
size	O
.	O
</s>
<s>
These	O
problems	O
can	O
be	O
parameterized	B-General_Concept
by	O
two	O
numbers	O
(	O
k	O
,	O
t	O
)	O
where	O
k	O
is	O
the	O
number	O
of	O
variables	O
per	O
clause	O
and	O
t	O
is	O
the	O
maximum	O
number	O
of	O
different	O
clauses	O
that	O
any	O
variable	O
can	O
appear	O
in	O
.	O
</s>
<s>
The	O
following	O
algorithm	O
can	O
be	O
shown	O
using	O
entropy	B-General_Concept
compression	I-General_Concept
to	O
find	O
such	O
a	O
solution	O
when	O
r	O
is	O
smaller	O
by	O
a	O
constant	O
factor	O
than	O
this	O
bound	O
:	O
</s>
<s>
The	O
name	O
"	O
entropy	B-General_Concept
compression	I-General_Concept
"	O
was	O
given	O
to	O
this	O
method	O
in	O
a	O
blog	O
posting	O
by	O
Terence	O
Tao	O
and	O
has	O
since	O
been	O
used	O
for	O
it	O
by	O
other	O
researchers	O
.	O
</s>
<s>
Since	O
the	O
discovery	O
of	O
the	O
entropy	B-General_Concept
compression	I-General_Concept
method	O
,	O
it	O
has	O
also	O
been	O
used	O
to	O
achieve	O
stronger	O
bounds	O
for	O
some	O
problems	O
than	O
would	O
be	O
given	O
by	O
the	O
Lovász	O
local	O
lemma	O
.	O
</s>
<s>
However	O
,	O
a	O
more	O
direct	O
argument	O
using	O
entropy	B-General_Concept
compression	I-General_Concept
shows	O
that	O
there	O
exists	O
a	O
coloring	O
using	O
only	O
4(Δ1 )	O
colors	O
,	O
and	O
moreover	O
this	O
coloring	O
can	O
be	O
found	O
in	O
randomized	O
polynomial	O
time	O
.	O
</s>
