<s>
(	O
1+	O
)	O
-approximate	O
nearest	B-Algorithm
neighbor	I-Algorithm
search	I-Algorithm
is	O
a	O
variant	O
of	O
the	O
nearest	B-Algorithm
neighbor	I-Algorithm
search	I-Algorithm
problem	O
.	O
</s>
<s>
A	O
solution	O
to	O
the	O
(	O
1+	O
)	O
-approximate	O
nearest	B-Algorithm
neighbor	I-Algorithm
search	I-Algorithm
is	O
a	O
point	O
or	O
multiple	O
points	O
within	O
distance	O
(	O
1+	O
)	O
from	O
a	O
query	O
point	O
,	O
where	O
is	O
the	O
distance	O
between	O
the	O
query	O
point	O
and	O
its	O
true	O
nearest	O
neighbor	O
.	O
</s>
<s>
Reasons	O
to	O
approximate	O
nearest	B-Algorithm
neighbor	I-Algorithm
search	I-Algorithm
include	O
the	O
space	O
and	O
time	O
costs	O
of	O
exact	O
solutions	O
in	O
high-dimensional	O
spaces	O
(	O
see	O
curse	B-Algorithm
of	I-Algorithm
dimensionality	I-Algorithm
)	O
and	O
that	O
in	O
some	O
domains	O
,	O
finding	O
an	O
approximate	O
nearest	O
neighbor	O
is	O
an	O
acceptable	O
solution	O
.	O
</s>
<s>
Approaches	O
for	O
solving	O
(	O
1+	O
)	O
-approximate	O
nearest	B-Algorithm
neighbor	I-Algorithm
search	I-Algorithm
include	O
kd-trees	B-Data_Structure
,	O
Locality	B-Algorithm
Sensitive	I-Algorithm
Hashing	I-Algorithm
and	O
brute	B-Algorithm
force	I-Algorithm
search	I-Algorithm
.	O
</s>
