<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
M-trees	B-Data_Structure
are	O
tree	B-Application
data	I-Application
structures	I-Application
that	O
are	O
similar	O
to	O
R-trees	B-Library
and	O
B-trees	B-Architecture
.	O
</s>
<s>
It	O
is	O
constructed	O
using	O
a	O
metric	O
and	O
relies	O
on	O
the	O
triangle	O
inequality	O
for	O
efficient	O
range	O
and	O
k-nearest	B-General_Concept
neighbor	I-General_Concept
(	O
k-NN	B-General_Concept
)	O
queries	B-Library
.	O
</s>
<s>
While	O
M-trees	B-Data_Structure
can	O
perform	O
well	O
in	O
many	O
conditions	O
,	O
the	O
tree	O
can	O
also	O
have	O
large	O
overlap	O
and	O
there	O
is	O
no	O
clear	O
strategy	O
on	O
how	O
to	O
best	O
avoid	O
overlap	O
.	O
</s>
<s>
In	O
addition	O
,	O
it	O
can	O
only	O
be	O
used	O
for	O
distance	O
functions	O
that	O
satisfy	O
the	O
triangle	O
inequality	O
,	O
while	O
many	O
advanced	O
dissimilarity	O
functions	O
used	O
in	O
information	B-Library
retrieval	I-Library
do	O
not	O
satisfy	O
this	O
.	O
</s>
<s>
As	O
in	O
any	O
tree-based	O
data	O
structure	O
,	O
the	O
M-tree	B-Data_Structure
is	O
composed	O
of	O
nodes	O
and	O
leaves	O
.	O
</s>
<s>
An	O
M-tree	B-Data_Structure
has	O
these	O
components	O
and	O
sub-components	O
:	O
</s>
<s>
Input	O
:	O
Node	O
of	O
M-Tree	B-Data_Structure
,	O
</s>
<s>
If	O
split	O
methods	O
arrives	O
to	O
a	O
node	O
that	O
is	O
not	O
the	O
root	O
of	O
the	O
tree	O
,	O
the	O
method	O
choose	O
two	O
new	O
routing	O
objects	O
from	O
,	O
re-arrange	O
every	O
routing	O
object	O
in	O
in	O
two	O
new	O
nodes	O
and	O
,	O
and	O
store	O
these	O
new	O
nodes	O
in	O
the	O
parent	B-Application
node	I-Application
of	O
original	O
.	O
</s>
<s>
Input	O
:	O
Node	O
of	O
M-Tree	B-Data_Structure
,	O
</s>
<s>
A	O
range	O
query	B-Library
is	O
where	O
a	O
minimum	O
similarity/maximum	O
distance	O
value	O
is	O
specified	O
.	O
</s>
<s>
,	O
the	O
range	O
query	B-Library
range( Q	O
,	O
r(Q )	O
)	O
selects	O
all	O
the	O
indexed	O
objects	O
such	O
that	O
.	O
</s>
<s>
Algorithm	O
RangeSearch	O
starts	O
from	O
the	O
root	B-Application
node	I-Application
and	O
recursively	O
traverses	O
all	O
the	O
paths	O
which	O
cannot	O
be	O
excluded	O
from	O
leading	O
to	O
qualifying	O
objects	O
.	O
</s>
<s>
k-nearest	B-General_Concept
neighbor	I-General_Concept
(	O
k-NN	B-General_Concept
)	O
query	B-Library
takes	O
the	O
cardinality	O
of	O
the	O
input	O
set	O
as	O
an	O
input	O
parameter	O
.	O
</s>
<s>
integer	O
k	O
≥	O
1	O
,	O
the	O
k-NN	B-General_Concept
query	B-Library
NN(Q, k )	O
selects	O
the	O
k	O
indexed	O
objects	O
which	O
have	O
the	O
shortest	O
distance	O
from	O
Q	O
,	O
according	O
to	O
the	O
distance	O
function	O
d	O
.	O
</s>
