<s>
A	O
BK-tree	B-Data_Structure
is	O
a	O
metric	B-Data_Structure
tree	I-Data_Structure
suggested	O
by	O
Walter	O
Austin	O
Burkhard	O
and	O
Robert	O
M	O
.	O
Keller	O
specifically	O
adapted	O
to	O
discrete	O
metric	O
spaces	O
.	O
</s>
<s>
Then	O
,	O
BK-tree	B-Data_Structure
is	O
defined	O
in	O
the	O
following	O
way	O
.	O
</s>
<s>
BK-trees	B-Data_Structure
can	O
be	O
used	O
for	O
approximate	B-Algorithm
string	I-Algorithm
matching	I-Algorithm
in	O
a	O
dictionary	O
.	O
</s>
<s>
The	O
BK-tree	B-Data_Structure
is	O
built	O
so	O
that	O
:	O
</s>
<s>
for	O
all	O
node	O
of	O
the	O
BK-tree	B-Data_Structure
,	O
the	O
weight	O
assigned	O
to	O
its	O
egress	O
arcs	O
are	O
distinct	O
;	O
</s>
<s>
The	O
insertion	O
primitive	O
is	O
used	O
to	O
populate	O
a	O
BK-tree	B-Data_Structure
according	O
to	O
a	O
discrete	O
metric	O
.	O
</s>
<s>
:	O
the	O
BK-tree	B-Data_Structure
;	O
</s>
<s>
Given	O
a	O
searched	O
element	O
,	O
the	O
lookup	O
primitive	O
traverses	O
the	O
BK-tree	B-Data_Structure
to	O
find	O
the	O
closest	O
element	O
of	O
.	O
</s>
<s>
The	O
key	O
idea	O
is	O
to	O
restrict	O
the	O
exploration	O
of	O
to	O
nodes	O
that	O
can	O
only	O
improve	O
the	O
best	O
candidate	O
found	O
so	O
far	O
by	O
taking	O
advantage	O
of	O
the	O
BK-tree	B-Data_Structure
organization	O
and	O
of	O
the	O
triangle	O
inequality	O
(	O
cut-off	O
criterion	O
)	O
.	O
</s>
<s>
:	O
the	O
BK-tree	B-Data_Structure
;	O
</s>
