<s>
A	O
relaxed	B-Data_Structure
K-d	I-Data_Structure
tree	I-Data_Structure
or	O
relaxed	O
K-dimensional	O
tree	O
is	O
a	O
data	O
structure	O
which	O
is	O
a	O
variant	O
of	O
K-d	B-Data_Structure
trees	I-Data_Structure
.	O
</s>
<s>
Unlike	O
K-d	B-Data_Structure
trees	I-Data_Structure
,	O
in	O
a	O
relaxed	B-Data_Structure
K-d	I-Data_Structure
tree	I-Data_Structure
,	O
the	O
discriminants	O
in	O
each	O
node	O
are	O
arbitrary	O
.	O
</s>
<s>
Relaxed	B-Data_Structure
K-d	I-Data_Structure
trees	I-Data_Structure
were	O
introduced	O
in	O
1998	O
.	O
</s>
<s>
A	O
relaxed	B-Data_Structure
K-d	I-Data_Structure
tree	I-Data_Structure
for	O
a	O
set	O
of	O
K-dimensional	O
keys	O
is	O
a	O
binary	O
tree	O
in	O
which	O
:	O
</s>
<s>
If	O
K	O
=	O
1	O
,	O
a	O
relaxed	B-Data_Structure
K-d	I-Data_Structure
tree	I-Data_Structure
is	O
a	O
binary	B-Language
search	I-Language
tree	I-Language
.	O
</s>
<s>
As	O
in	O
a	O
K-d	B-Data_Structure
tree	I-Data_Structure
,	O
a	O
relaxed	B-Data_Structure
K-d	I-Data_Structure
tree	I-Data_Structure
of	O
size	O
n	O
induces	O
a	O
partition	O
of	O
the	O
domain	O
D	O
into	O
n+1	O
regions	O
,	O
each	O
corresponding	O
to	O
a	O
leaf	O
in	O
the	O
K-d	B-Data_Structure
tree	I-Data_Structure
.	O
</s>
<s>
The	O
average	O
time	O
complexities	O
in	O
a	O
relaxed	B-Data_Structure
K-d	I-Data_Structure
tree	I-Data_Structure
with	O
n	O
records	O
are	O
:	O
</s>
