<s>
In	O
data	B-General_Concept
processing	I-General_Concept
R*	B-Data_Structure
-trees	I-Data_Structure
are	O
a	O
variant	O
of	O
R-trees	B-Library
used	O
for	O
indexing	O
spatial	O
information	O
.	O
</s>
<s>
R*	B-Data_Structure
-trees	I-Data_Structure
have	O
slightly	O
higher	O
construction	O
cost	O
than	O
standard	O
R-trees	B-Library
,	O
as	O
the	O
data	O
may	O
need	O
to	O
be	O
reinserted	O
;	O
but	O
the	O
resulting	O
tree	O
will	O
usually	O
have	O
a	O
better	O
query	O
performance	O
.	O
</s>
<s>
Like	O
the	O
standard	O
R-tree	B-Library
,	O
it	O
can	O
store	O
both	O
point	O
and	O
spatial	O
data	O
.	O
</s>
<s>
Minimization	O
of	O
both	O
coverage	O
and	O
overlap	O
is	O
crucial	O
to	O
the	O
performance	O
of	O
R-trees	B-Library
.	O
</s>
<s>
The	O
R*	B-Data_Structure
-tree	I-Data_Structure
uses	O
the	O
same	O
algorithm	O
as	O
the	O
regular	O
R-tree	B-Library
for	O
query	O
and	O
delete	O
operations	O
.	O
</s>
<s>
When	O
inserting	O
,	O
the	O
R*	B-Data_Structure
-tree	I-Data_Structure
uses	O
a	O
combined	O
strategy	O
.	O
</s>
<s>
When	O
splitting	O
,	O
the	O
R*	B-Data_Structure
-tree	I-Data_Structure
uses	O
a	O
topological	O
split	O
that	O
chooses	O
a	O
split	O
axis	O
based	O
on	O
perimeter	O
,	O
then	O
minimizes	O
overlap	O
.	O
</s>
<s>
In	O
addition	O
to	O
an	O
improved	O
split	O
strategy	O
,	O
the	O
R*	B-Data_Structure
-tree	I-Data_Structure
also	O
tries	O
to	O
avoid	O
splits	O
by	O
reinserting	O
objects	O
and	O
subtrees	O
into	O
the	O
tree	O
,	O
inspired	O
by	O
the	O
concept	O
of	O
balancing	O
a	O
B-tree	B-Architecture
.	O
</s>
<s>
Worst	O
case	O
query	O
and	O
delete	O
complexity	O
are	O
thus	O
identical	O
to	O
the	O
R-Tree	B-Library
.	O
</s>
<s>
The	O
insertion	O
strategy	O
to	O
the	O
R*	B-Data_Structure
-tree	I-Data_Structure
is	O
with	O
more	O
complex	O
than	O
the	O
linear	O
split	O
strategy	O
(	O
)	O
of	O
the	O
R-tree	B-Library
,	O
but	O
less	O
complex	O
than	O
the	O
quadratic	O
split	O
strategy	O
(	O
)	O
for	O
a	O
page	O
size	O
of	O
objects	O
and	O
has	O
little	O
impact	O
on	O
the	O
total	O
complexity	O
.	O
</s>
<s>
The	O
total	O
insert	O
complexity	O
is	O
still	O
comparable	O
to	O
the	O
R-tree	B-Library
:	O
reinsertions	O
affect	O
at	O
most	O
one	O
branch	O
of	O
the	O
tree	O
and	O
thus	O
reinsertions	O
,	O
comparable	O
to	O
performing	O
a	O
split	O
on	O
a	O
regular	O
R-tree	B-Library
.	O
</s>
<s>
So	O
on	O
overall	O
,	O
the	O
complexity	O
of	O
the	O
R*	B-Data_Structure
-tree	I-Data_Structure
is	O
the	O
same	O
as	O
that	O
of	O
a	O
regular	O
R-tree	B-Library
.	O
</s>
