<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
approximate	B-Algorithm
string	I-Algorithm
matching	I-Algorithm
(	O
often	O
colloquially	O
referred	O
to	O
as	O
fuzzy	B-Algorithm
string	I-Algorithm
searching	I-Algorithm
)	O
is	O
the	O
technique	O
of	O
finding	O
strings	O
that	O
match	O
a	O
pattern	O
approximately	O
(	O
rather	O
than	O
exactly	O
)	O
.	O
</s>
<s>
The	O
problem	O
of	O
approximate	B-Algorithm
string	I-Algorithm
matching	I-Algorithm
is	O
typically	O
divided	O
into	O
two	O
sub-problems	O
:	O
finding	O
approximate	O
substring	O
matches	O
inside	O
a	O
given	O
string	O
and	O
finding	O
dictionary	O
strings	O
that	O
match	O
the	O
pattern	O
approximately	O
.	O
</s>
<s>
One	O
possible	O
definition	O
of	O
the	O
approximate	B-Algorithm
string	I-Algorithm
matching	I-Algorithm
problem	O
is	O
the	O
following	O
:	O
Given	O
a	O
pattern	O
string	O
and	O
a	O
text	O
string	O
,	O
find	O
a	O
substring	O
in	O
T	O
,	O
which	O
,	O
of	O
all	O
substrings	O
of	O
T	O
,	O
has	O
the	O
smallest	O
edit	O
distance	O
to	O
the	O
pattern	O
P	O
.	O
</s>
<s>
A	O
better	O
solution	O
,	O
which	O
was	O
proposed	O
by	O
Sellers	O
,	O
relies	O
on	O
dynamic	B-Algorithm
programming	I-Algorithm
.	O
</s>
<s>
Computing	O
the	O
E(x,y )	O
array	O
takes	O
O(mn )	O
time	O
with	O
the	O
dynamic	B-Algorithm
programming	I-Algorithm
algorithm	O
,	O
while	O
the	O
backwards-working	O
phase	O
takes	O
O( n+m	O
)	O
time	O
.	O
</s>
<s>
When	O
matching	O
database	O
relates	O
to	O
a	O
large	O
scale	O
of	O
data	O
,	O
the	O
O(mn )	O
time	O
with	O
the	O
dynamic	B-Algorithm
programming	I-Algorithm
algorithm	O
cannot	O
work	O
within	O
a	O
limited	O
time	O
.	O
</s>
<s>
Widely	O
used	O
algorithms	O
are	O
based	O
on	O
filter-verification	O
,	O
hashing	O
,	O
Locality-sensitive	B-Algorithm
hashing	I-Algorithm
(	O
LSH	O
)	O
,	O
Tries	B-General_Concept
and	O
other	O
greedy	O
and	O
approximation	O
algorithms	O
.	O
</s>
<s>
Traditionally	O
,	O
approximate	B-Algorithm
string	I-Algorithm
matching	I-Algorithm
algorithms	O
are	O
classified	O
into	O
two	O
categories	O
:	O
on-line	B-Algorithm
and	O
off-line	O
.	O
</s>
<s>
With	O
on-line	B-Algorithm
algorithms	I-Algorithm
the	O
pattern	O
can	O
be	O
processed	O
before	O
searching	O
but	O
the	O
text	O
cannot	O
.	O
</s>
<s>
In	O
other	O
words	O
,	O
on-line	B-Algorithm
techniques	O
do	O
searching	O
without	O
an	O
index	O
.	O
</s>
<s>
Early	O
algorithms	O
for	O
on-line	B-Algorithm
approximate	O
matching	O
were	O
suggested	O
by	O
Wagner	O
and	O
Fisher	O
and	O
by	O
Sellers	O
.	O
</s>
<s>
Both	O
algorithms	O
are	O
based	O
on	O
dynamic	B-Algorithm
programming	I-Algorithm
but	O
solve	O
different	O
problems	O
.	O
</s>
<s>
Sellers	O
 '	O
algorithm	O
searches	O
approximately	O
for	O
a	O
substring	O
in	O
a	O
text	O
while	O
the	O
algorithm	O
of	O
Wagner	O
and	O
Fisher	O
calculates	O
Levenshtein	O
distance	O
,	O
being	O
appropriate	O
for	O
dictionary	O
fuzzy	B-Algorithm
search	I-Algorithm
only	O
.	O
</s>
<s>
On-line	B-Algorithm
searching	O
techniques	O
have	O
been	O
repeatedly	O
improved	O
.	O
</s>
<s>
famous	O
improvement	O
is	O
the	O
bitap	B-Algorithm
algorithm	I-Algorithm
(	O
also	O
known	O
as	O
the	O
shift-or	B-Algorithm
and	O
shift-and	B-Algorithm
algorithm	O
)	O
,	O
which	O
is	O
very	O
efficient	O
for	O
relatively	O
short	O
pattern	O
strings	O
.	O
</s>
<s>
The	O
Bitap	B-Algorithm
algorithm	I-Algorithm
is	O
the	O
heart	O
of	O
the	O
Unix	B-Application
searching	O
utility	B-Application
agrep	B-Device
.	O
</s>
<s>
A	O
review	O
of	O
on-line	B-Algorithm
searching	O
algorithms	O
was	O
done	O
by	O
G	O
.	O
Navarro	O
.	O
</s>
<s>
Although	O
very	O
fast	O
on-line	B-Algorithm
techniques	O
exist	O
,	O
their	O
performance	O
on	O
large	O
data	O
is	O
unacceptable	O
.	O
</s>
<s>
Text	O
preprocessing	O
or	O
indexing	B-Application
makes	O
searching	O
dramatically	O
faster	O
.	O
</s>
<s>
Today	O
,	O
a	O
variety	O
of	O
indexing	B-Application
algorithms	O
have	O
been	O
presented	O
.	O
</s>
<s>
Among	O
them	O
are	O
suffix	B-Architecture
trees	I-Architecture
,	O
metric	B-Data_Structure
trees	I-Data_Structure
and	O
n-gram	B-Language
methods	O
.	O
</s>
<s>
A	O
detailed	O
survey	O
of	O
indexing	B-Application
techniques	O
that	O
allows	O
one	O
to	O
find	O
an	O
arbitrary	O
substring	O
in	O
a	O
text	O
is	O
given	O
by	O
Navarro	O
et	O
al	O
.	O
</s>
<s>
Common	O
applications	O
of	O
approximate	O
matching	O
include	O
spell	B-Application
checking	I-Application
.	O
</s>
<s>
Record	B-General_Concept
linkage	I-General_Concept
is	O
a	O
common	O
application	O
where	O
records	O
from	O
two	O
disparate	O
databases	O
are	O
matched	O
.	O
</s>
<s>
They	O
require	O
different	O
algorithms	O
,	O
such	O
as	O
acoustic	B-Algorithm
fingerprinting	I-Algorithm
.	O
</s>
<s>
A	O
common	O
command-line	O
tool	O
fzf	B-Algorithm
is	O
often	O
used	O
to	O
integrate	O
approximate	O
string	O
searching	O
into	O
various	O
command-line	O
applications	O
.	O
</s>
