<s>
The	O
Priority	B-Data_Structure
R-tree	I-Data_Structure
is	O
a	O
worst-case	O
asymptotically	O
optimal	O
alternative	O
to	O
the	O
spatial	O
tree	B-Application
R-tree	B-Library
.	O
</s>
<s>
The	O
prioritized	O
R-tree	B-Library
is	O
essentially	O
a	O
hybrid	O
between	O
a	O
k-dimensional	B-Data_Structure
tree	I-Data_Structure
and	O
a	O
r-tree	B-Library
in	O
that	O
it	O
defines	O
a	O
given	O
object	O
's	O
N-dimensional	O
bounding	B-Data_Structure
volume	I-Data_Structure
(	O
called	O
Minimum	O
Bounding	O
Rectangles	O
-	O
MBR	O
)	O
as	O
a	O
point	O
in	O
N-dimensions	O
,	O
represented	O
by	O
the	O
ordered	O
pair	O
of	O
the	O
rectangles	O
.	O
</s>
<s>
The	O
term	O
prioritized	O
arrives	O
from	O
the	O
introduction	O
of	O
four	O
priority-leaves	O
that	O
represents	O
the	O
most	O
extreme	O
values	O
of	O
each	O
dimensions	O
,	O
included	O
in	O
every	O
branch	O
of	O
the	O
tree	B-Application
.	O
</s>
<s>
Before	O
answering	O
a	O
window-query	B-Library
by	O
traversing	O
the	O
sub-branches	O
,	O
the	O
prioritized	O
R-tree	B-Library
first	O
checks	O
for	O
overlap	O
in	O
its	O
priority	O
nodes	O
.	O
</s>
<s>
The	O
sub-branches	O
are	O
traversed	O
(	O
and	O
constructed	O
)	O
by	O
checking	O
whether	O
the	O
least	O
value	O
of	O
the	O
first	O
dimension	O
of	O
the	O
query	B-Library
is	O
above	O
the	O
value	O
of	O
the	O
sub-branches	O
.	O
</s>
<s>
I/Os	O
,	O
where	O
N	O
is	O
the	O
number	O
of	O
d-dimensional	O
(	O
hyper	O
-	O
)	O
rectangles	O
stored	O
in	O
the	O
R-tree	B-Library
,	O
B	O
is	O
the	O
disk	O
block	O
size	O
,	O
and	O
T	O
is	O
the	O
output	O
size	O
.	O
</s>
