<s>
An	O
R+	B-Data_Structure
tree	I-Data_Structure
is	O
a	O
method	O
for	O
looking	O
up	O
data	O
using	O
a	O
location	O
,	O
often	O
(	O
x	O
,	O
y	O
)	O
coordinates	O
,	O
and	O
often	O
for	O
locations	O
on	O
the	O
surface	O
of	O
the	O
earth	O
.	O
</s>
<s>
Fundamentally	O
,	O
an	O
R+	B-Data_Structure
tree	I-Data_Structure
is	O
a	O
tree	B-Application
data	I-Application
structure	I-Application
,	O
a	O
variant	O
of	O
the	O
R	B-Library
tree	I-Library
,	O
used	O
for	O
indexing	O
spatial	O
information	O
.	O
</s>
<s>
R+	B-Data_Structure
trees	I-Data_Structure
are	O
a	O
compromise	O
between	O
R-trees	B-Library
and	O
kd-trees	B-Data_Structure
:	O
they	O
avoid	O
overlapping	O
of	O
internal	O
nodes	O
by	O
inserting	O
an	O
object	O
into	O
multiple	O
leaves	O
if	O
necessary	O
.	O
</s>
<s>
Minimal	O
coverage	O
reduces	O
the	O
amount	O
of	O
"	O
dead	O
space	O
"	O
(	O
empty	O
area	O
)	O
which	O
is	O
covered	O
by	O
the	O
nodes	O
of	O
the	O
R-tree	B-Library
.	O
</s>
<s>
R+	B-Data_Structure
trees	I-Data_Structure
differ	O
from	O
R	B-Library
trees	I-Library
in	O
that	O
:	O
nodes	O
are	O
not	O
guaranteed	O
to	O
be	O
at	O
least	O
half	O
filled	O
,	O
the	O
entries	O
of	O
any	O
internal	O
node	O
do	O
not	O
overlap	O
,	O
and	O
an	O
object	O
ID	O
may	O
be	O
stored	O
in	O
more	O
than	O
one	O
leaf	O
node	O
.	O
</s>
<s>
A	O
single	O
path	O
is	O
followed	O
and	O
fewer	O
nodes	O
are	O
visited	O
than	O
with	O
the	O
R-tree	B-Library
.	O
</s>
<s>
Since	O
rectangles	O
are	O
duplicated	O
,	O
an	O
R+	B-Data_Structure
tree	I-Data_Structure
can	O
be	O
larger	O
than	O
an	O
R	B-Library
tree	I-Library
built	O
on	O
same	O
data	O
set	O
.	O
</s>
<s>
Construction	O
and	O
maintenance	O
of	O
R+	B-Data_Structure
trees	I-Data_Structure
is	O
more	O
complex	O
than	O
the	O
construction	O
and	O
maintenance	O
of	O
R	B-Library
trees	I-Library
and	O
other	O
variants	O
of	O
the	O
R	B-Library
tree	I-Library
.	O
</s>
