<s>
The	O
cover	B-Data_Structure
tree	I-Data_Structure
is	O
a	O
type	O
of	O
data	B-General_Concept
structure	I-General_Concept
in	O
computer	B-General_Concept
science	I-General_Concept
that	O
is	O
specifically	O
designed	O
to	O
facilitate	O
the	O
speed-up	O
of	O
a	O
nearest	B-Algorithm
neighbor	I-Algorithm
search	I-Algorithm
.	O
</s>
<s>
It	O
is	O
a	O
refinement	O
of	O
the	O
Navigating	O
Net	O
data	B-General_Concept
structure	I-General_Concept
,	O
and	O
related	O
to	O
a	O
variety	O
of	O
other	O
data	B-General_Concept
structures	I-General_Concept
developed	O
for	O
indexing	O
intrinsically	O
low-dimensional	O
data	O
.	O
</s>
<s>
Each	O
level	O
C	O
in	O
the	O
cover	B-Data_Structure
tree	I-Data_Structure
has	O
three	O
important	O
properties	O
:	O
</s>
<s>
Like	O
other	O
metric	B-Data_Structure
trees	I-Data_Structure
the	O
cover	B-Data_Structure
tree	I-Data_Structure
allows	O
for	O
nearest	B-Algorithm
neighbor	I-Algorithm
searches	I-Algorithm
in	O
where	O
is	O
a	O
constant	O
associated	O
with	O
the	O
dimensionality	O
of	O
the	O
dataset	O
and	O
n	O
is	O
the	O
cardinality	O
.	O
</s>
<s>
Unlike	O
other	O
metric	B-Data_Structure
trees	I-Data_Structure
,	O
the	O
cover	B-Data_Structure
tree	I-Data_Structure
has	O
a	O
theoretical	O
bound	O
on	O
its	O
constant	O
that	O
is	O
based	O
on	O
the	O
dataset	O
's	O
expansion	O
constant	O
or	O
doubling	O
constant	O
(	O
in	O
the	O
case	O
of	O
approximate	O
NN	O
retrieval	O
)	O
.	O
</s>
<s>
Although	O
cover	B-Data_Structure
trees	I-Data_Structure
provide	O
faster	O
searches	O
than	O
the	O
naive	O
approach	O
,	O
this	O
advantage	O
must	O
be	O
weighed	O
with	O
the	O
additional	O
cost	O
of	O
maintaining	O
the	O
data	B-General_Concept
structure	I-General_Concept
.	O
</s>
<s>
In	O
a	O
naive	O
approach	O
adding	O
a	O
new	O
point	O
to	O
the	O
dataset	O
is	O
trivial	O
because	O
order	O
does	O
not	O
need	O
to	O
be	O
preserved	O
,	O
but	O
in	O
a	O
cover	B-Data_Structure
tree	I-Data_Structure
it	O
can	O
take	O
time	O
.	O
</s>
<s>
The	O
cover	B-Data_Structure
tree	I-Data_Structure
uses	O
implicit	O
representation	O
to	O
keep	O
track	O
of	O
repeated	O
points	O
.	O
</s>
