<s>
In	O
computing	O
,	O
the	O
count	B-Algorithm
–	I-Algorithm
min	I-Algorithm
sketch	I-Algorithm
(	O
CM	B-Algorithm
sketch	I-Algorithm
)	O
is	O
a	O
probabilistic	B-General_Concept
data	B-General_Concept
structure	I-General_Concept
that	O
serves	O
as	O
a	O
frequency	O
table	O
of	O
events	O
in	O
a	O
stream	O
of	O
data	O
.	O
</s>
<s>
It	O
uses	O
hash	B-Error_Name
functions	I-Error_Name
to	O
map	O
events	O
to	O
frequencies	O
,	O
but	O
unlike	O
a	O
hash	B-Algorithm
table	I-Algorithm
uses	O
only	O
sub-linear	O
space	O
,	O
at	O
the	O
expense	O
of	O
overcounting	O
some	O
events	O
due	O
to	O
collisions	B-Algorithm
.	O
</s>
<s>
The	O
count	B-Algorithm
–	I-Algorithm
min	I-Algorithm
sketch	I-Algorithm
was	O
invented	O
in	O
2003	O
by	O
Graham	O
Cormode	O
and	O
S	O
.	O
Muthu	O
Muthukrishnan	O
and	O
described	O
by	O
them	O
in	O
a	O
2005	O
paper	O
.	O
</s>
<s>
Count	B-Algorithm
–	I-Algorithm
min	I-Algorithm
sketches	I-Algorithm
are	O
essentially	O
the	O
same	O
data	B-General_Concept
structure	I-General_Concept
as	O
the	O
counting	B-Algorithm
Bloom	I-Algorithm
filters	I-Algorithm
introduced	O
in	O
1998	O
by	O
Fan	O
et	O
al	O
.	O
</s>
<s>
However	O
,	O
they	O
are	O
used	O
differently	O
and	O
therefore	O
sized	O
differently	O
:	O
a	O
count	B-Algorithm
–	I-Algorithm
min	I-Algorithm
sketch	I-Algorithm
typically	O
has	O
a	O
sublinear	O
number	O
of	O
cells	O
,	O
related	O
to	O
the	O
desired	O
approximation	O
quality	O
of	O
the	O
sketch	O
,	O
while	O
a	O
counting	B-Algorithm
Bloom	I-Algorithm
filter	I-Algorithm
is	O
more	O
typically	O
sized	O
to	O
match	O
the	O
number	O
of	O
elements	O
in	O
the	O
set	O
.	O
</s>
<s>
The	O
goal	O
of	O
the	O
basic	O
version	O
of	O
the	O
count	B-Algorithm
–	I-Algorithm
min	I-Algorithm
sketch	I-Algorithm
is	O
to	O
consume	O
a	O
stream	O
of	O
events	O
,	O
one	O
at	O
a	O
time	O
,	O
and	O
count	O
the	O
frequency	O
of	O
the	O
different	O
types	O
of	O
events	O
in	O
the	O
stream	O
.	O
</s>
<s>
The	O
actual	O
sketch	O
data	B-General_Concept
structure	I-General_Concept
is	O
a	O
two-dimensional	O
array	O
of	O
columns	O
and	O
rows	O
.	O
</s>
<s>
Associated	O
with	O
each	O
of	O
the	O
rows	O
is	O
a	O
separate	O
hash	B-Error_Name
function	I-Error_Name
;	O
the	O
hash	B-Error_Name
functions	I-Error_Name
must	O
be	O
pairwise	O
independent	O
.	O
</s>
<s>
When	O
a	O
new	O
event	O
of	O
type	O
arrives	O
we	O
update	O
as	O
follows	O
:	O
for	O
each	O
row	O
of	O
the	O
table	O
,	O
apply	O
the	O
corresponding	O
hash	B-Error_Name
function	I-Error_Name
to	O
obtain	O
a	O
column	O
index	O
.	O
</s>
<s>
An	O
inner	O
product	O
query	O
asks	O
for	O
the	O
inner	O
product	O
between	O
the	O
histograms	O
represented	O
by	O
two	O
count	B-Algorithm
–	I-Algorithm
min	I-Algorithm
sketches	I-Algorithm
,	O
and	O
.	O
</s>
<s>
Small	O
modifications	O
to	O
the	O
data	B-General_Concept
structure	I-General_Concept
can	O
be	O
used	O
to	O
sketch	O
other	O
different	O
stream	O
statistics	O
.	O
</s>
<s>
Like	O
the	O
Count	B-Algorithm
sketch	I-Algorithm
,	O
the	O
Count	B-Algorithm
–	I-Algorithm
min	I-Algorithm
sketch	I-Algorithm
is	O
a	O
linear	O
sketch	O
.	O
</s>
<s>
One	O
potential	O
problem	O
with	O
the	O
usual	O
min	O
estimator	O
for	O
count	B-Algorithm
–	I-Algorithm
min	I-Algorithm
sketches	I-Algorithm
is	O
that	O
they	O
are	O
biased	O
estimators	O
of	O
the	O
true	O
frequency	O
of	O
events	O
:	O
they	O
may	O
overestimate	O
,	O
but	O
never	O
underestimate	O
the	O
true	O
count	O
in	O
a	O
point	O
query	O
.	O
</s>
<s>
Furthermore	O
,	O
while	O
the	O
min	O
estimator	O
works	O
well	O
when	O
the	O
distribution	O
is	O
highly	O
skewed	O
,	O
other	O
sketches	O
such	O
as	O
the	O
Count	B-Algorithm
sketch	I-Algorithm
based	O
on	O
means	O
are	O
more	O
accurate	O
when	O
the	O
distribution	O
is	O
not	O
sufficiently	O
skewed	O
.	O
</s>
