<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
Ukkonen	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
is	O
a	O
linear-time	O
,	O
online	B-Algorithm
algorithm	I-Algorithm
for	O
constructing	O
suffix	B-Architecture
trees	I-Architecture
,	O
proposed	O
by	O
Esko	O
Ukkonen	O
in	O
1995	O
.	O
</s>
<s>
The	O
algorithm	O
begins	O
with	O
an	O
implicit	O
suffix	B-Architecture
tree	I-Architecture
containing	O
the	O
first	O
character	O
of	O
the	O
string	O
.	O
</s>
<s>
This	O
order	O
addition	O
of	O
characters	O
gives	O
Ukkonen	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
its	O
"	O
on-line	O
"	O
property	O
.	O
</s>
<s>
While	O
generating	O
suffix	B-Architecture
tree	I-Architecture
using	O
Ukkonen	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
,	O
we	O
will	O
see	O
implicit	O
suffix	B-Architecture
tree	I-Architecture
in	O
intermediate	O
steps	O
depending	O
on	O
characters	O
in	O
string	O
S	O
.	O
In	O
implicit	O
suffix	B-Architecture
trees	I-Architecture
,	O
there	O
will	O
be	O
no	O
edge	O
with	O
$	O
(	O
or	O
any	O
other	O
termination	O
character	O
)	O
label	O
and	O
no	O
internal	O
node	O
with	O
only	O
one	O
edge	O
going	O
out	O
of	O
it	O
.	O
</s>
<s>
Ukkonen	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
constructs	O
an	O
implicit	O
suffix	B-Architecture
tree	I-Architecture
T	O
for	O
each	O
prefix	O
1	O
...	O
i	O
of	O
S	O
(	O
S	O
being	O
the	O
string	O
of	O
length	O
n	O
)	O
.	O
</s>
<s>
You	O
can	O
find	O
the	O
following	O
characteristics	O
in	O
a	O
suffix	B-Architecture
tree	I-Architecture
that	O
uses	O
Ukkonen	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
:	O
</s>
<s>
Implicit	O
suffix	B-Architecture
tree	I-Architecture
T	O
is	O
built	O
on	O
top	O
of	O
implicit	O
suffix	B-Architecture
tree	I-Architecture
T	O
.	O
</s>
<s>
At	O
any	O
given	O
time	O
,	O
Ukkonen	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
builds	O
the	O
suffix	B-Architecture
tree	I-Architecture
for	O
the	O
characters	O
seen	O
so	O
far	O
and	O
so	O
it	O
has	O
on-line	O
property	O
,	O
allowing	O
the	O
algorithm	O
to	O
have	O
an	O
execution	O
time	O
of	O
O(n )	O
.	O
</s>
<s>
Ukkonen	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
is	O
divided	O
into	O
n	O
phases	O
(	O
one	O
phase	O
for	O
each	O
character	O
in	O
the	O
string	O
with	O
length	O
n	O
)	O
.	O
</s>
<s>
Suffix	O
extension	O
is	O
all	O
about	O
adding	O
the	O
next	O
character	O
into	O
the	O
suffix	B-Architecture
tree	I-Architecture
built	O
so	O
far	O
.	O
</s>
<s>
The	O
naive	O
implementation	O
for	O
generating	O
a	O
suffix	B-Architecture
tree	I-Architecture
going	O
forward	O
requires	O
or	O
even	O
time	O
complexity	O
in	O
big	O
O	O
notation	O
,	O
where	O
is	O
the	O
length	O
of	O
the	O
string	O
.	O
</s>
<s>
To	O
better	O
illustrate	O
how	O
a	O
suffix	B-Architecture
tree	I-Architecture
using	O
Ukkonen	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
is	O
constructed	O
,	O
we	O
can	O
use	O
the	O
following	O
example	O
:	O
</s>
